symmetry reductions and exact solutions of the 2 1 dimensional jaulent miodek equation by applying the direct symmetry method we obtain the symmetry reductions group invariant solutions and some new exact solutions of the 2 1 dimensional jaulent miodek equation which include jacobi elliptic function solutions airy function solutions trigonometric function solutions hyperbolic function solutions and so on

consecutive rosochatius deformations of the neumann system consecutive rosochatius deformations of the neumann system are investigated it is first shown that different realizations of a classical sl 2 gaudin magnet model yield different integrable hamiltonian systems then an algorithm of constructing infinitely many symplectic realizations of sl 2 algebra from a known one is presented and thus the neumann system can be deformed consecutively the second rosochatius deformation of the neumann system is taken as an illustrative example to show that the deformed systems admit separations of variables and may be linearized on the jacobi variety

explicit solutions of the 2 1 dimensional akns shallow water wave equation with variable coefficients abstract using an improved direct reduction method we find the equivalence transformations of 2 1 dimensional akns shallow water wave equation with variable coefficients and obtain the corresponding relationship between explicit solutions of akns equation and those of the corresponding reduced equation in addition we get some new explicit solutions of akns equation by applying lie symmetry method

an improved γ riccati backlund transformation and its applications for the inhomogeneous nonlinear schrodinger model from plasma physics and nonlinear optics abstract the inhomogeneous nonlinear schrodinger type nls model from certain plasmas and optical fibers is investigated with symbolic computation an improved riccati backlund transformation r bt is presented which can generate successively a hierarchy of solutions through algebraic manipulations based on the improved r bt the darboux transformation is obtained the analytic one two soliton like solutions are presented and the physical characteristics of the influences of the coefficient parameters on the propagation of the soliton pulses are discussed graphically

continuous robust control design for nonlinear uncertain systems without a priori knowledge of control direction in this paper a robust control scheme is proposed for a class of nonlinear systems that have not only additive nonlinear uncertainties but also unknown multiplicative signs these signs are called control directions since they represent effectively the direction of motion under any given control except for the unknown control directions the class of systems satisfy the generalized matching conditions nonlinear robust control is designed to identify on line unknown control directions and to guarantee global stability of uniform ultimate boundedness without the knowledge of nonlinear dynamics except their size bounding functions it is also shown that the proposed robust control can be made continuous through utilizing the so called shifting laws that change smoothly and accordingly the signs of robust controls and that no matter what time constants and gains of the shifting laws are global stability is always ensured the analysis and design is done using lyapunov s direct method

application of he s variational iteration method to nonlinear jaulent miodek equations and comparing it with adm instead of finding a small parameter for solving nonlinear problems through perturbation method a new analytical method called he s variational iteration method vim is introduced to be applied to solve nonlinear jaulent miodek coupled kdv and coupled mkdv equations in this article in this method general lagrange multipliers are introduced to construct correction functionals for the problems the multipliers can be identified optimally via the variational theory the results are compared with exact solutions

quasi periodic solution of the 2 1 dimensional boussinesq burgers soliton equation abstract a 2 1 dimensional bossinesq burgers soliton equation is proposed which has a affinitive connection with the boussinesq burgers soliton hierarchy through a natural nonlinearization of the boussinesq burgers s eigenvalue problems a finite dimensional hamiltonian system is obtained and is proved to be completely integrable in liouville sense the abel jacobi coordinates are constructed to straighten out the hamiltonian flows from which the quasi periodic solutions of the 2 1 dimensional boussinesq burgers equation are derived by resorting to the riemann theta functions

new explicit traveling wave solutions for three nonlinear evolution equations abstract in this paper using the extended tanh function method new explicit traveling wave solutions including rational solutions for three nonlinear evolution equations are obtained with the aid of mathematica

algebro geometric solution of the 2 1 dimensional burgers equation with a discrete variable the quasiperiodic solution of the 2 1 dimensional burgers equation with a discrete variable is obtained through three steps a decomposition into a symplectic map plus two finite dimensional hamiltonian systems b straightening out of both the discrete and the continuous flows in the jacobian variety c inversion into the original variables inner relation with the modified kadomtsev petviashvili equation is presented the explicit theta function solutions for these two 2 1 integrable models are given

a generalized g g expansion method and its applications to nonlinear evolution equations in this paper a generalized g g expansion method and its algorithm are proposed by studying wang s g g expansion method and constructing a first order nonlinear ordinary differential equation with a third degree nonlinear term being concise and straightforward the method is applied to combined kdv mkdv equation and coupled jaulent miodek equation as a result some new exact travelling wave solutions are obtained which include solitary wave solutions triangular periodic wave solutions exponential solutions complex travelling solutions and rational solutions this method can also be applied to other nonlinear evolution equations in mathematical physics

particle simulations of the kac model of the boltzmann equation abstract we consider a simplified mathematical model of the boltzmann equation which was introduced by kac a quasi monte carlo particle simulation using t m s nets is described the particle movement is shown to be an evaluation of the volume of a subset of i4 0 1 4 an error bound for quasi monte carlo approximation of the volume of a generalized quadrant set is derived when a t m s net is used convergence of the simulation is proved when the particles are reordered according to their velocity in every time step quasi monte carlo and monte carlo particle simulations are compared in computational experiments the results indicate that quasi monte carlo simulation outperforms standard monte carlo approaches

some algebro geometric solutions for the coupled modified kadomtsev petviashvili equations arising from the neumann type systems a treatment is described for getting some algebro geometric solutions of the coupled modified kadomtsev petviashvili cmkp equations and a hierarchy of 1 1 dimensional integrable nonlinear evolution equations inlees by using the neumann type systems through three steps i according to the nonlinearization of lax pair the cmkp equations and the 1 1 dimensional inlees are reduced to a family of compatible neumann type systems on a symplectic submanifold whose involutive solutions give rise to the finite parametric solutions of the inlees in both 2 1 and 1 1 dimensions ii from the holomorphic differentials and the abel map on a hyperelliptic curve of riemman surface the abel jacobi variables are introduced to straighten out the neumann type flows the 1 1 and 2 1 dimensional flows giving the abel jacobi solutions iii based on the riemann theorem and the trace formulas the jacobi inversion is applied to the straightened flows for getting some new algebro geometric solutions of the cmkp equations and the 1 1 dimensional integrable hierarchy

asymptotic behavior of the periodic wave solution for the 3 1 dimensional kadomtsev petviashvili equation abstract in this paper the one and two periodic wave solutions for the 3 1 dimensional kadomtsev petviashvili equation are presented by means of the hirota s bilinear method and the riemann theta function the rigorous proofs on asymptotic behaviors of these two solutions are given that soliton solution can be obtained from the periodic wave solution in an appropriate limiting procedure

stabilization of linear time invariant interval systems via constant state feedback control this paper investigates the stabilization problem of linear uncertain systems via constant state feedback control the systems under consideration contain time invariant uncertain parameters whose values are unknown but bounded in given compact sets and are thus called interval systems the criterion for the asymptotic stability of the closed loop system obtained when a state feedback control is applied is that all the eigenvalues of the resulting system matrix are in the strict left half of the complex plane first the author shows that to insure an interval system stabilizable some entries of the system matrices must be sign invariant more precisely the number of the least required sign invariant entries in system matrices is equal to the system order then the author studies the stabilizability of a set of interval systems called standard systems which contain sufficient numbers of sign invariant entries in proper locations after dividing all standard systems into some subsets by the uncertainty locations the author then derives necessary and sufficient conditions under which every system in a subset is stabilizable regardless of its parameter varying bounds the conditions show that all uncertain entries in system matrices should form a particular geometrical pattern called a generalized antisymmetric stepwise configuration for an interval system satisfying the stabilizability conditions a computational control design procedure is also provided and illustrated via an example the result is further generalized for nonstandard systems via linear transformation

multi soliton and pfaffian solutions of a 2 1 dimensional nonlinear evolution equation via the jaulent miodek hierarchy abstract under investigation in this paper is a 2 1 dimensional nonlinear evolution equation generated by the jaulent miodek hierarchy via the hirota bilinear method multi soliton solutions of such equation are obtained soliton propagation and interactions are analyzed and both the elastic and inelastic interactions are seen with some parameters selected furthermore it is proved that the equation possesses the n soliton solutions expressed in terms of gramm type pfaffian and can be written in the form of a pfaffian identity

quasi periodic solutions of the modified kadomtsev petviashvili equation the 2 1 dimensional modified kadomtsev petviashvili equation is decomposed into systems of integrable ordinary differential equations resorting to the nonlinearization of lax pairs abel jacobi coordinates are introduced to straighten the flows from which quasi periodic solutions of the modified kadomtsev petviashvili equation are obtained in terms of riemann theta functions

symplectic realizations and action angle coordinates for the lie poisson system of dirac hierarchy abstract in this paper the relations among four finite dimensional hamiltonian systems associated with the dirac hierarchy are studied via three poisson maps from the standard symplectic structures to the lie poisson structure of lie algebra sl 2 it has shown that the canonical hamiltonian systems in the standard symplectic structures are the different symplectic realizations of the lie poisson hamiltonian system the action angle coordinates and the jacobi inversion problem for the lie poisson hamiltonian systems are also investigated in detail

disturbance observer based robust mixed h2 h fuzzy tracking control for hypersonic vehicles this paper introduces a disturbance observer do based mixed h2 h robust fuzzy tracking control design for the longitudinal dynamics of a generic hypersonic vehicle hv with modeled and unmodeled disturbances a takagisugeno ts fuzzy model is firstly employed to approximate the nonlinear dynamics of hv subsequently based on the fuzzy model a do is constructed to estimate the modeled disturbance next by integrating the hv dynamics the tracking error integral and the disturbance estimation error dynamics an augmented system is established for the control design then a do based mixed h2 h robust fuzzy control design is developed to ensure the asymptotic stability as well as the mixed h2 h control performance of the augmented system the proposed control scheme includes a fuzzy tracking controller with state feedback plus the tracking error integral a robust nonlinear compensator for eliminating the matched part of the compound disturbance consisting of the unmodeled disturbance and fuzzy modeling error and a do based compensator for the modeled disturbance cancellation the outcome of the do based mixed h2 h robust fuzzy control problem is formulated in terms of linear matrix inequalities lmis furthermore by utilizing the existing lmi optimization technique a suboptimal controller is obtained in the sense of minimizing an upper bound of h2 performance finally simulation results on an hv demonstrate the effectiveness of the proposed design method

quasiperiodic waves and asymptotic behavior for bogoyavlenskii s breaking soliton equation in 2 1 dimensions based on a multidimensional riemann theta function the hirota bilinear method is extended to explicitly construct multiperiodic quasiperiodic wave solutions for the 2 1 dimensional bogoyavlenskii breaking soliton equation among these periodic waves the one periodic waves are well known cnoidal waves their surface pattern is one dimensional and often they are used as one dimensional models of periodic waves in shallow water the two periodic biperiodic waves are a direct generalization of one periodic waves their surface pattern is two dimensional that is they have two independent spatial periods in two independent horizontal directions the two periodic waves may be considered to represent periodic waves in shallow water without the assumption of one dimensionality a limiting procedure is presented to analyze asymptotic behavior of the one and two periodic waves in details the exact relations between the periodic wave solutions and the well known soliton solutions are established it is rigorously shown that the periodic wave solutions tend to the soliton solutions under a small amplitude limit

hidden symmetries and exact solutions of integro differential jaulent miodek evolution equation use of the adjoint method to obtain optimal lie vectors a reduction of the jm equation to ordinary differential equations and detection of lie symmetries test if these symmetries are hidden analysis and plot of results comparison with previous work in the field analytical solutions of a 2 1 dimensional nonlinear model using the jaulent miodek hierarchy are investigated following a similarity reduction procedure for this adjoint lie matrices are first evaluated and an extensive list of optimal lie vectors is obtained the systematic reduction of jaulent miodek evolution equation to lower number of variables leads to hidden symmetries and new solutions

integrable decompositions of a symmetric matrix kaup newell equation and a symmetric matrix derivative nonlinear schrodinger equation it is shown that the reduction conditions in the spectral problems of soliton equations can be replaced by more equations of eigenfunctions based on this the method of nonlinearization of spectral problem is extended to soliton equations with reduction conditions integrable decompositions of a symmetric matrix kaup newell equation and a symmetric matrix derivative nonlinear schrodinger equation are constructed

low discrepancy sequences for solving the boltzmann equation abstract some new quasi monte carlo methods for the solution of the boltzmann equation in a simplified case are described the errors of the methods are estimated by means of the discrepancies of the sequences used for performing the monte carlo quadratures their accuracy is assessed through computation of effective errors in an example where an exact solution is known

further results on the observer design problem abstract in this paper the observer design problem for nonlinear systems is considered sufficient lyapunov like conditions are presented for the existence of a nonlinear observer the theory we develop considerably improves and extends the results of our recent work 14

decentralized variable structure control for tracking in non linear systems the problem of tracking time varying trajectories in non linear systems is considered these trajectories could be generated on line by a reference model the problem is tackled by considering the overall system as a set of decentralized linear sub systems which can be modelled as a set of double integrators and treating the non linearities as uncertainties with known bounds on their magnitudes a variable structure controller is designed based on the theory of uncertain dynamical systems the system is shown to track a class of trajectories generated by the reference mode a set of double integrators to within a specified tolerance some analysis is presented to explain the dynamic behaviour of the closed loop system and bounds are derived linking the rate of convergence and the tracking ability to system parameters such as available control and magnitude of the uncertainty simulation results are presented to validate the conclusions

quasiperiodic solutions of jaulent miodek equations with a negative flow a hierarchy of new nonlinear evolution equations is proposed which are composed of the positive and negative jaulent miodek flows based on the theory of algebraic curve the corresponding flows are straightened under the abel jacobi coordinates the meromorphic function the baker akhiezer vector and the hyperelliptic curve kn are introduced by which quasiperiodic solutions of the first two nonlinear evolution equations in the hierarchy are constructed according to the asymptotic properties and the algebro geometric characters of and kn

the deduction of the lax representation for constrained flows from the adjoint representation for x and tn finite dimensional hamiltonian systems obtained from the decompositions of zero curvature equations it is shown that their lax representations can be deduced directly from the adjoint representations of the auxiliary linear problems as a consequence the zero curvature representation for soliton hierarchy with source is presented

n soliton and quasi periodic solutions of the kdv6 equations abstract a hierarchy of new nonlinear evolution equations which contains the well known kdv6 equation is proposed based on the inverse scattering method n soliton solutions of the first four equations including the kdv6 equation in this hierarchy are derived finally quasi periodic solutions of the kdv6 equations are constructed according to the theory of algebraic curve

symmetry and similarity solutions of variable coefficients generalized zakharov kuznetsov equation abstract in this paper we propose a compatibility method of finding symmetry and similarity reduction of partial differential equations being a simple example the 2 1 dimensional variable coefficients zakharov kuznetsov equation is considered as a result we derive the symmetries and corresponding reductions of the zakharov kuznetsov equation at the same time some new similarity solutions are obtained the method can also be applied to other nonlinear evolution equations in mathematical physics

from integrable to superintegrable it is shown that the presence of multiple eigenvalue parameters may result in the superintegrability of the restricted soliton flows the restricted akns flow the neumann system and the restricted mkdv flow with an eigenvalue parameter whose multiplicity is greater than two are demonstrated to be superintegrable

robust semi global output tracking for nonlinear singularly perturbed systems in this work a robust controller design methodology for a broad class of singularly perturbed nonlinear systems with time varying uncertainties is developed when the fast subsystem is stabilizable and the slow subsystem is input output linearizable with input to state stable iss inverse dynamics the developed state feedback controller guarantees boundedness of the trajectories of the closed loop system and robust output tracking with arbitrary degree of asymptotic attenuation of the effect of uncertainty on the output for initial conditions and uncertainties in an arbitrarily large compact set so long as the singular perturbation parameter is sufficiently small the controller is a continuous function of the state of the system and its construction requires the knowledge of bounding functions on the size of uncertainty the developed method is applied to a non isothermal continuous stirred tank reactor with fast jacket dynamics

a generalized ablowitz ladik hierarchy multi hamiltonian structure and darboux transformation starting from a discrete spectral problem we derive a hierarchy of nonlinear discrete equations which includes the ablowitz ladik hierarchy and a new hierarchy as special cases especially we investigate in detail the integrability and resolvability of the new hierarchy it is shown that the new hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure a darboux transformation is established for a typical discrete system in the new hierarchy with the help of the gauge transformation of its lax pair as applications of the darboux transformation new exact solutions of the discrete system are explicitly given

neumann type integrable reduction for nonlinear evolution equations in 1 1 and 2 1 dimensions a family of new neumann type systems is given in view of the nonlinearization technique realizing the variable separation of the modified jaulent miodek hierarchy and a new coupled modified kadomtsev petviashvili equation on the symplectic submanifold tsn 1 by two casimir functions and a special solution of the lenard eigenvalue equation we deduce the lax moser matrix of the neumann type systems that yields integrals of motion and the constrained hamiltonians whose vector fields are tangent to tsn 1 based on the dirac poisson bracket and a lax equation on tsn 1 a new systematic way is proposed to prove the liouville integrability of a family of neumann type systems synchronously the dirac poisson bracket and the generating function are used to reveal the explicit relation between infinite dimensional integrable systems and neumann type systems and then we point out that compatible solutions of neumann type systems yield the finite parametric solutions of 1 1 and 2 1 dimensional integrable nonlinear

on different integrable systems sharing the same nondynamical r matrix in a recent paper zhijun qiao and ruguang zhou phys lett a 235 35 1997 the amazing fact was reported that a discrete and a continuous integrable system share the same r matrix with the interesting property of being nondynamical now we present three further pairs of different continuous integrable systems sharing the same r matrix again being nondynamical the first pair is the finite dimensional constrained system fdcs of the famous akns hierarchy and the dirac hierarchy the second pair is the fdcs of the well known geodesic flows on the ellipsoid and the heisenberg spin chain hierarchy and the third pair is the fdcs of one hierarchy studied by xianguo geng phys lett a 162 375 1992 and another hierarchy proposed by zhijun qiao phys lett a 192 316 1994 all those fdcss possess lax representations and from the viewpoint of r matrix can be shown to be completely integrable in liouville s sense

finite gap solutions of 2 1 dimensional integrable nonlinear evolution equations generated by the neumann systems each soliton equation in the korteweg de vries kdv hierarchy the 2 1 dimensional breaking soliton equation and the 2 1 dimensional caudrey dodd gibbon kotera sawada cdgks equation are reduced to two or three neumann systems on the tangent bundle tsn 1 of the unit sphere sn 1 the lax moser matrix for the neumann systems of degree n 1 is deduced in view of the mckean trubowitz identity and a bilinear generating function whose favorite characteristic accounts for the problem of the genus of riemann surface matching to the number of elliptic variables from the lax moser matrix the constrained hamiltonians in the sense of dirac poisson bracket for all the neumann systems are written down in a uniform recursively determined by integrals of motion the involution of integrals of motion and constrained hamiltonians is completed on tsn 1 by using a lax equation and their functional independence is displayed over a dense open subset of tsn 1 by a direct calculation which contribute to the liouville integ

practical stabilization of nonlinear uncertain dynamic systems with bounded controllers we address the problem of practically stabilizing nonlinear and or uncertain continuous time dynamic systems when the norm of the control input is subject to a given fixed bound we consider a class of systems whose nominal part is linear and whose nonlinear uncertain part does not satisfy the matching condition in this treatment no statistical information regarding the uncertainties is needed only a norm bound on each nonlinear uncertain quantity is assumed we propose a bounded state feedback controller whose design incorporates elements from both variable structure control theory and the deterministic control methodology using the second method of lyapunov we obtain sliding domains regions of uniform ultimate boundedness and estimates of the domain of attraction for systems employing this controller the closed loop stability analysis as well as the design of the controller is facilitated by introducing a special coordinate transformation the approach is illustrated by a numerical example

the finite band solution of the jaulent miodek equation a method to construct the finite band solution to the soliton equation is presented we take the jaulent miodek equation as an example with the use of the nonlinearization of lax pair the jaulent miodek equation is decomposed into two finite dimensional integrable systems whose properties are studied from the view of an r matrix then through solving these finite dimensional integrable systems the finite band solution of the jaulent miodek equation is obtained

design of softer robust nonlinear control laws abstract we show that the lyapunov function used in backstepping feedback designs for uncertain nonlinear systems leads to unnecessarily hard control laws having undesirable high gain properties we present a new lyapunov function and use it to design softer control laws which exhibit the high gain properties to a much lesser extent we show that the soft designs eliminate the chattering exhibited by the hard designs and achieve the same or better performance with less control effort

a hierarchy of garnier rosochatius systems a hierarchy of hamiltonian systems including the garnier rosochatius system as the first member is introduced this hierarchy of hamiltonian systems is proved to be completely integrable and the corresponding flows are linearized on the jacobi variety of the associated hyperelliptic curve in addition a relation between these flows and the kdv equation is found and the connection with finite gap solution of kdv equation is shown

the quasi periodic solutions of mixed kdv equations the quasi periodic solutions of mixed kdv equations are constructed to derive the solutions we introduce the mixed finite dimensional integrable hamiltonian systems fdihs which are linearized on the jacobi variety of the associated hyperelliptic curve a relation between the fdihs and the mixed kdv equations is revealed based on this relation we construct the quasi periodic solutions for the mixed kdv equations with aid of the riemann theta function the quasi periodic solutions for the kdv6 equation and the negative order kdv equation are obtained as special members of the mixed kdv equations

robust control of cascaded and individually feedback linearizable nonlinear systems abstract feedback linearization technique is applied to design robust controllers for a class of nonlinear uncertain systems every system in the class is a series connection of finite number of nonlinear subsystems which are individually feedback linearizable and have significant but matched nonlinear functional uncertainties the key difference between this work and existing robust results is that the matching conditions and the existence of feedback linearization transformation are only required individually for each subsystem a constructive robust control design procedure is proposed for the unique control in the overall system the procedure is conceptually simple and contains three steps first perform input output feedback linearization for all individual subsystems second design fictitious robust controllers for inputs of each subsystem as if the subsystem had an independent control finally a mapping is developed which maps the individual fictitious controls recursively into the unique control of the overall system since neither the matching conditions nor feedback linearization are required for the overall system this becomes the broadest class of nonlinear uncertain or known systems for which a robust regular tracking control can be constructed using feedback linearization method global stability of the overall system is always guaranteed

a quasi monte carlo method for the boltzmann equation a new quasi monte carlo method for solving the boltzmann equation in a simplified case is described the analysis is restricted to a spatially homogeneous and isotropic gas in addition the molecular model only involves isotropic scattering the scheme makes use of particles and combines an euler scheme with numerical integrations the sequence which is used for the quadratures must possess some symmetry properties which prescribe energy conservation for colliding particles the error of the method is estimated by means of the discrepancy of the sequence which performs the quadratures an algorithm for generating convenient sequences is proposed in an example where an exact solution is known the computation of effective errors is included introduction rarefied gas flows are usually simulated by monte carlo techniques besides the successful direct simulation monte carlo dsmc method of bird 2 another scheme was derived by nanbu 14 from the boltzmann equation itself a drawback of both schemes are numerical fluctuations caused by the use of pseudorandom numbers an improved monte carlo scheme which reduces fluctuations has recently been developed at the university of kaiserslautern 1 it will be referred to as the kmc scheme a fully deterministic method for solving the boltzmann equation is proposed here the constraints on the analysis are the following we consider an infinite spatially homogeneous and isotropic gas the velocity distribution is radially symmetric the molecular model is characterized by isotropic scattering the differential cross section a depends only on the relative speed g and not on the deflection angle in addition we assume that ga g is some nonnegative nondecreasing and bounded function the hypothesis on the cross section allows physically relevant models such as the vhs model of bird 3 when a cutoff is used in earlier communications io i i the simplest choice ga g equals a constant was considered a deterministic version of the scheme of nanbu that we called the low discrepancy ld method was described an error analysis was proposed and it was shown that the ld method outperforms the original scheme of nanbu in a test case where an exact solution is known received march 1 1990 1980 mathematics subject classification 1985 revision primary 65m15 secondary 65c05 llk38 1991 american mathematical society 0025 5718 91 l 00 25 per page

a quasi monte carlo approach to particle simulation of the heat equation the convergence of the monte carlo method for numerical integration can often be improved by replacing random numbers with more uniformly distributed numbers known as quasi random in this paper the convergence of monte carlo particle simulation is studied when these quasi random sequences are used for the one dimensional heat equation discretized in both space and time convergence is proved for a quasi random simulation using reordering of the particles according to their position experimental results are presented for the spatially continuous heat equation in one and two dimensions the results indicate that a significant improvement in both magnitude of error and convergence rate can be achieved over standard monte carlo simulations for certain low dimensional problems

practical stabilization of a class of uncertain nonlinear systems abstract in this paper the problem of robust control of a class of nonlinear systems with internal and input channel uncertainties is addressed the proposed control algorithm reflects the two level structure of the plant and guarantees the system uniform asymptotic stability with respect to an arbitrary neighbourhood of the nominal system stability point

group invariant solutions of the 2 1 dimensional cubic schrodinger equation we use lie point symmetries of the 2 1 dimensional cubic schrodinger equation to obtain new analytic solutions in a systematic manner we present an analysis of the reduced odes and in particular show that although the original equation is not integrable they typically can belong to the class of painleve type equations

the positive and negative camassa holm γ hierarchies zero curvature representations bi hamiltonian structures and algebro geometric solutions in this paper we extend the camassa holm ch equation to two different hierarchies of nonlinear evolution equations by resorting to two lenard recursion sequences one is of positive order ch hierarchy including a harry dym type equation while the other is of negative order ch hierarchy of integrodifferential equations with nonzero integration constants including the ch equation we provide the zero curvature representations for both hierarchies by solving a key matrix equation moreover the lenard sequences are used to construct a lax matrix that satisfies a stationary zero curvature equation which enables us to establish bi hamiltonian structures for both hierarchies by applying trace identity in addition the lenard sequence and lax pair are used to systematically derive the its matveev trace formula and the dubrovin type equations associated with the ch equation the hyperelliptic curve and abel jacobi coordinates are then introduced to linearize the associated flow from which the algebro geometric solutions to the ch equation are constructed by using standard jacobi inversion technique in this paper we extend the camassa holm ch equation to two different hierarchies of nonlinear evolution equations by resorting to two lenard recursion sequences one is of positive order ch hierarchy including a harry dym type equation while the other is of negative order ch hierarchy of integrodifferential equations with nonzero integration constants including the ch equation we provide the zero curvature representations for both hierarchies by solving a key matrix equation moreover the lenard sequences are used to construct a lax matrix that satisfies a stationary zero curvature equation which enables us to establish bi hamiltonian structures for both hierarchies by applying trace identity in addition the lenard sequence and lax pair are used to systematically derive the its matveev trace formula and the dubrovin type equations associated with the ch equation the hyperelliptic curve and abel jacobi coordinates are then introduced to linearize the associated flow from which the a

from the special 2 1 toda lattice to the kadomtsev petviashvili equation the nonlinearization of the eigenvalue problems associated with the toda hierarchy and the coupled korteweg de vries kdv hierarchy leads to an integrable symplectic map s and an integrable hamiltonian system h0 respectively it is proved that s and h0 have the same integrals hk the quasi periodic solution of the 2 1 dimensional kadomtsev petviashvili equation is split into three hamiltonian systems h0 h1 h2 while that of the special 2 1 dimensional toda equation is separated into h0 h1 plus the discrete flow generated by the symplectic map s a clear evolution picture of various flows is given through the window of abel jacobi coordinates the explicit theta function solutions are obtained by resorting to this separation technique

symmetry reductions and similarity solutions of the 3 1 dimensional breaking soliton equation abstract using the compatibility method we obtain three types of symmetry of the 3 1 dimensional breaking soliton equation by solving the corresponding characteristic equations associated with symmetry equations symmetry reductions of the 3 1 dimensional breaking soliton equation are given first then some special types of similarity solutions are constructed

continuous state feedback guaranteeing uniform ultimate boundedness for uncertain dynamic systems we consider a dynamic system containing uncertain elements only the set of possible values of these uncertainties is known based on this information a class of state feedback controls is proposed in order to guarantee uniform ultimate boundedness of every system response within an arbitrarily small neighborhood of the zero state these feedback controls are continuous functions of the state

memoryless static output feedback sliding mode control for nonlinear systems with delayed disturbances in this technical note a local stabilization problem for nonlinear systems with disturbances which are dependent on time varying delay phenomena is studied an appropriate transformation is introduced to express the system in regular form which facilitates both design and analysis then sufficient conditions are developed based on a lyapunov razumikhin approach such that the sliding motion is uniformly asymptotically or exponentially stable a static output feedback control law independent of the time delay is synthesized to guarantee reachability of the sliding mode the accessible bounds on the disturbances are fully used in the control design to reduce the conservatism a simulation example shows the effectiveness of the approach

lie algebras and the stability of nonlinear systems lie algebras and the cartan decomposition are used to study the stability of pseudo linear systems of differential equations

quasi periodic solution of a new 2 1 dimensional coupled soliton equation a new 2 1 dimensional integrable soliton equation is proposed which has a close connection with the levi soliton hierarchy through the nonlinearization of the levi eigenvalue problems we obtain a finite dimensional integrable system the abel jacobi coordinates are constructed to straighten out the hamiltonian flows by which the solutions of both the 1 1 and 2 1 levi equations are obtained through linear superpositions an inversion procedure gives the quasi periodic solution in the original coordinates in terms of the riemann theta functions

negative order korteweg de vries equations in this paper based on the regular korteweg de vries kdv system we study negative order kdv nkdv equations particularly their hamiltonian structures lax pairs conservation laws and explicit multisoliton and multikink wave solutions thorough bilinear backlund transformations the nkdv equations studied in our paper are differential and actually derived from the first member in the negative order kdv hierarchy the nkdv equations are not only gauge equivalent to the camassa holm equation through reciprocal transformations but also closely related to the ermakov pinney systems and the kupershmidt deformation the bi hamiltonian structures and a darboux transformation of the nkdv equations are constructed with the aid of trace identity and their lax pairs respectively the single and double kink wave and bell soliton solutions are given in an explicit formula through the darboux transformation the one kink wave solution is expressed in the form of tanh while the one bell soliton is in the form of sech and both forms are very standard the collisions of two kink wave and two bell soliton solutions are analyzed in detail and this singular interaction differs from the regular kdv equation multidimensional binary bell polynomials are employed to find bilinear formulation and backlund transformations which produce n soliton solutions a direct and unifying scheme is proposed for explicitly building up quasiperiodic wave solutions of the nkdv equations furthermore the relations between quasiperiodic wave solutions and soliton solutions are clearly described finally we show the quasiperiodic wave solution convergent to the soliton solution under some limit conditions

separation of variables in the classical integrable sl 3 magnetic chain there are two fundamental problems studied by the theory of hamiltonian integrable systems integration of equations of motion and construction of action angle variables a third problem however should be added to the list separation of variables though much simpler thant the two others it has important relations to quantum integrability separation of variables is constructed for thesl 3 magnetic chain an example of an integrable model associated to a nonhyperelliptic algebraic curve

finite band solutions of the classical boussinesq burgers equations the classical boussinesq burgers hierarchy is decomposed into two systems of solvable ordinary differential equations with the help of the lax representations of stationary evolution equations from which the finite band solutions of the higher order classical boussinesq burgers equations are obtained

output feedback decentralized control of large scale systems using weighted sensitivity functions minimization this paper considers the problem of achieving stability and desired dynamical transient behavior for linear large scale systems by decentralized control it can be done by making the effects of the interconnections between the subsystems arbitrarily small sufficient conditions for stability and diagonal dominance of the closed loop system are introduced these conditions are in terms of decentralized subsystems and directly make a constructive h control design possible a mixed h pole region placement is suggested such that by assigning the closed loop eigenvalues of the isolated subsystems appropriately the eigenvalues of the overall closed loop system are assigned in desirable range the designs are illustrated by an example

1 soliton solution and conservation laws for the jaulent miodekequation with power law nonlinearity abstract this paper obtains the 1 soliton solution of the jaulent miodek equation with power law nonlinearity the solitary wave ansatz is used to obtain the soliton solution to this equation subsequently the conserved quantities are computed using the invariance and multiplier approach based on the well known result that the euler lagrange operator annihilates the total divergence

brief robust control of nonlinear systems with parametric uncertainty probabilistic robustness analysis and synthesis for nonlinear systems with uncertain parameters are presented monte carlo simulation is used to estimate the likelihood of system instability and violation of performance requirements subject to variations of the probabilistic system parameters stochastic robust control synthesis searches the controller design parameter space to minimize a cost that is a function of the probabilities that design criteria will not be satisfied the robust control design approach is illustrated by a simple nonlinear example a modified feedback linearization control is chosen as controller structure and the design parameters are searched by a genetic algorithm to achieve the tradeoff between stability and performance robustness

painleve analysis of the damped driven nonlinear schrodinger equation on applique les tests de painleve a l equation iu t u xx 2 u 2 u a x t u b x t ou a et b sont des fonctions analytiques de x et t pour etudier sous quelles conditions l equation peut etre completement integrable

liouville integrability of the finite dimensional hamiltonian systems derived from principal chiral field for finite dimensional hamiltonian systems derived from 1 1 dimensional integrable systems if they have lax representations then the lax operator creates a set of conserved integrals when these conserved integrals are in involution it is believed quite popularly that there will be enough functionally independent ones among them to guarantee the liouville integrability of the hamiltonian systems at least for those derived from physical problems in this article we give a counterexample based on the u 2 principal chiral field it is proved that the finite dimensional hamiltonian systems derived from the u 2 principal chiral field are liouville integrable moreover their lax operator gives a set of involutive conserved integrals but they are not enough to guarantee the integrability of the hamiltonian systems

periodic wave solutions of the boussinesq equation the boussinesq equation usually arises in a physical problem as a long wave equation the present work extends the search of periodic wave solutions for it the hirota bilinear method and riemann theta function are employed in the process we also analyse the asymptotic property of periodic waves in detail furthermore it is of interest to note that well known soliton solutions can be reduced from the periodic wave solutions

an algebro geometric solution for a hamiltonian system with application to dispersive long wave equation by using an iterative algebraic method we derive from a spectral problem a hierarchy of nonlinear evolution equations associated with dispersive long wave equation it is shown that the hierarchy is integrable in liouville sense and possesses bi hamiltonian structure two commutators with zero curvature and lax representations for the hierarchy are constructed respectively by using two different systematic methods under a bargmann constraint the spectral is nonlinearized to a completely integrable finite dimensional hamiltonian system by introducing the abel jacobi coordinates an algebro geometric solution for the dispersive long wave equation is derived by resorting to the riemann theta function

optimal and suboptimal feedback controls for a class of nonlinear systems abstract in this paper we consider a class of nonlinear regulator problems in which the control appears linearly using an approach similar to that given for the classical linear quadratic regulator problem it is shown in 1 that the optimal feedback control can be expressed as a function of the solution of an algebraic riccati equation at each point in the state space more precisely it is shown that by solving a riccati equation at a given point in the state space the optimal feedback control at that particular point is readily obtained in this paper our first aim is to investigate stability of the resulting closed loop system second a simple computational scheme for constructing a suboptimal control is suggested we then consider the problem of stabilizing the system when it is subjected to bounded noise for illustration two examples are used to test the effectiveness of the proposed computational schemes

nonlinearization of the lax pairs for discrete ablowitz ladik hierarchy abstract the discrete ablowitz ladik hierarchy with four potentials and the hamiltonian structures are derived under a constraint between the potentials and eigenfunctions the nonlinearization of the lax pairs associated with the discrete ablowitz ladik hierarchy leads to a new symplectic map and a class of finite dimensional hamiltonian systems the generating function of the integrals of motion is presented by which the symplectic map and these finite dimensional hamiltonian systems are further proved to be completely integrable in the liouville sense each member in the discrete ablowitz ladik hierarchy is decomposed into a hamiltonian system of ordinary differential equations plus the discrete flow generated by the symplectic map

variable structure robust control of uncertain time delay systems abstract this paper introduces a variable structure output feedback robust control for uncertain time delay systems new types of switching manifolds with integral terms are implemented to consider larger class of linear systems by overcoming both the observability constraints of the reduced order system and the kimura davison condition two types of control laws are introduced by which an estimate of a region of asymptotic stability to the origin and a region of attraction to the switching manifold are defined

bounded amplitude performance of switched lpv systems with applications to hybrid systems this paper discusses recent results on multiple linear agent control for systems satisfying a bounded amplitude performance constraint the plant is assumed to be a linear parameter varying lpv system scheduled along a nominal parameter trajectory in this respect the control problem represents a plant operating between a prespecified set of operating conditions linear controllers are designed at setpoints along this scheduling trajectory to satisfy bounded amplitude performance constraints this paper discusses an approach to analyze the switched system behavior under practical assumptions on the structure of the switching rule the approach combines the scheduling parameter with lpv system properties to derive bounds on the switching behavior of the system these estimates are then used to construct a logical model of the switched system behavior in the form of a timed automaton in this respect this paper presents a way of extracting logical models of continuous time system behavior

a quasi monte carlo scheme using nets for a linear boltzmann equation a quasi monte carlo particle simulation for solving a linear boltzmann equation is constructed and a convergence proof is given the analysis is restricted to the three dimensional equation in the space homogeneous case and the velocity domain is normalized to be i 3 0 1 3 a particle simulation is described it combines a euler scheme in time with quasi monte carlo integration in velocity space the quadratures use 0 m s nets which are sets with a very regular distribution behavior the particles are reordered according to the components of their velocity at each time step a deterministic error bound is obtained finally numerical experiments are presented for some test problems where an exact solution is known the accuracy of the quasi monte carlo scheme is compared with a standard monte carlo algorithm the results show an improvement in both magnitude of error and convergence rate of quasi monte carlo over monte carlo approach

linear and nonlinear stabilizing continuous controllers of uncertain dynamical systems including state delay the problem of robust stabilization of a class of time varying dynamical systems with disturbance uncertain parameters and a bounded time varying state delay is considered two classes of stabilizing continuous controllers are proposed the proposed controllers can guarantee the existence of the solution to the dynamical system in the usual sense and can also be directly implemented in the practical control problems moreover since the proposed controllers are completely independent of the time delay which is only assumed to be any nonnegative bounded and continuous function the results developed in this note are applicable to a class of dynamical systems with uncertain time delays finally a numerical example is given to demonstrate the validity of the results

integrable rosochatius deformations of the restricted soliton flows a method to construct integrable rosochatius deformations of the restricted soliton flows in the setup of lax formulation is presented the integrable rosochatius deformations of the restricted soliton flows such as the restricted ablowitz kaup newell segur flow the restricted tu meng flow the restricted tu flow with neumann type constraints and the restricted modified korteweg de vries flow together with their lax representations are presented in addition a lax representation of the jacobi rosochatius system is obtained

a simple direct method to find equivalence transformations of a generalized nonlinear schrodinger equation and a generalized kdv equation a simple direct method is presented to find equivalence transformations of nonlinear mathematical physics equations by using the direct method we obtain the continuous equivalence transformations of a class of nonlinear schroequations with variable coefficients and a family of nonlinear kdv equations with variable coefficients for the nonlinear schrodinger equations with variable coefficients the equivalence transformations obtained by the direct method coincide in nature with those obtained via the infinitesimal lie criterion but our computation is much simpler

quasi monte carlo integration the standard monte carlo approach to evaluating multidimensional integrals using pseudo random integration nodes is frequently used when quadrature methods are too difficult or expensive to implement as an alternative to the random methods it has been suggested that lower error and improved convergence may be obtained by replacing the pseudo random sequences with more uniformly distributed sequences known as quasi random in this paper quasi random halton sobol and faure and pseudo random sequences are compared in computational experiments designed to determine the effects on convergence of certain properties of the integrand including variance variation smoothness and dimension the results show that variation which plays an important role in the theoretical upper bound given by the koksma hlawka inequality does not affect convergence while variance the determining factor in random monte carlo is shown to provide a rough upper bound but does not accurately predict performance in general quasi monte carlo methods are superior to random monte carlo but the advantage may be slight particularly in high dimensions or for integrands that are not smooth for discontinuous integrands we derive a bound which shows that the exponent for algebraic decay of the integration error from quasi monte carlo is only slightly larger than 1 2 in high dimensions more 21 refs 6 figs 5 tabs less

letter to the editor on the exponential stability of a class of nonlinear systems including delayed perturbations in this letter the problem of robust stabilization of a class of nonlinear dynamical systems with delayed perturbations is considered based on the stability of the nominal systems a new stabilizing control law for exponential stability of the system is designed using lyapunov stability theory

the direct symmetry method and its application in variable coefficients schrodinger equation by using a direct transformation the variable coefficients schrodinger equation is changed to two nonlinear partial differential equations with variable coefficients we consider the two differential equations and derive different forms of symmetry by the direct symmetry method at last some symmetry reductions and explicit solutions of the variable coefficients schrodinger equation are obtained in terms of similarity solutions of the two differential equations

error bounds for quasi monte carlo integration with nets we analyze the error introduced by approximately calculating the s dimensional lebesgue measure of a jordan measurable subset of i s 0 1 s we give an upper bound for the error of a method using a t m s net which is a set with a very regular distribution behavior when the subset of i s is defined by some function of bounded variation on i s 1 the error is estimated by means of the variation of the function and the discrepancy of the point set which is used a sharper error bound is established when a t m s net is used finally a lower bound of the error is given for a method using a 0 m s net the special case of the 2 dimensional hammersley point set is discussed

fuzzy dynamical system approach for a dual parameter hybrid order robust control design abstract robust control for uncertain dynamical systems is considered the uncertainty is assumed to be bounded and the fuzzy set theory is adopted to describe the bound a new dual parameter hybrid order robust control design is then proposed in two steps first a class of robust controls is designed taking the advantage of the flexibility in choosing the order and a design parameter the controls are deterministic and are not if then fuzzy rules based deterministic performance including uniform boundedness and uniform ultimate boundedness for the controlled systems is guaranteed second a fuzzy set theoretic based performance index consisting of average and steady state system performance and control cost is proposed a constrained optimization problem is formulated with the intension of minimizing the performance index the objective of the optimization problem is to search for the optimal choice of dual parameters that minimizes the performance index we show that the solution to the optimization problem always exists as a result the resulting control design achieves two concurrent goals guaranteeing deterministic performance as well as minimizing the performance index the theory is illustrated by an unmanned aerial vehicle uav system control design

a comparative study of pseudo and quasi random sequences for the solution intergral equations a numerical study for the solution of integral equations using random numbers from congruential generators and the halton and the faure sequences is presented the results indicate that for high precision monte carlo quasi random sequences yield better results in general the relative performance of the quasi random sequences is better with monte carlo schemes which reduce the dimensionality of the problem

optimal tracking control for large scale interconnected systems with time delays this paper considers an infinite horizon optimal tracking control problem for a class of large scale interconnected systems with state time delays by using the successive approximation approach two iteration sequences of vector differential equations are constructed meanwhile the large scale interconnected system is decomposed into finite decoupled subsystems the existence and uniqueness of the optimal solution is proved as well as the convergence of the solution sequence by finite iterations of the solution sequence a suboptimal tracking control law is obtained a reduced order reference input observer is designed to make the feedforward term of the optimal tracking control law physically realizable a numerical example shows that the presented algorithm is effective and easy to implement

quasi periodic wave solution and asymptotic behavior for the 2 1 dimensional toda lattice equation abstract one and two periodic wave solutions for the 2 1 dimensional toda lattice equation are presented based on the hirota bilinear method and the riemann theta function the asymptotic behaviors of these two solutions are considered and the rigorous proof is given that the periodic wave solutions tend to the soliton solutions in an appropriate limiting procedure

algebro geometric solutions for the gerdjikov ivanov hierarchy this paper is dedicated to provide theta function representations of algebro geometric solutions and related crucial quantities for the gerdjikov ivanov gi hierarchy our main tools include the polynomial recursive formalism the hyperelliptic curve with finite number of genus the baker akhiezer functions the meromorphic function the dubrovin type equations for auxiliary divisors and the associated trace formulas with the help of these tools the explicit representations of the baker akhiezer functions the meromorphic function and the algebro geometric solutions are obtained for the entire gi hierarchy

on ultimate boundedness control of uncertain systems in the absence of matching assumptions this paper describes an approach to ultimate boundedness control under hypotheses less stringent than heretofore required instead of imposing the so called matching conditions of previous authors a certain decomposition of the dynamics is performed the resulting decomposed system has two parts a matched portion and a mismatched portion a certain measure of mismatch m is defined and it is shown that effective control is possible as long as m does not exceed some critical mismatch threshold m it is seen that this threshold depends on the choice of feedback hence it becomes possible to investigate the tradeoffs between the size of the mismatch threshold and the sizes of the feedback gains which achieve the desired ultimate boundedness of solutions