conformal covariantization of moyal lax operators a covariant approach to the conformal property associated with moyal lax operators is given by identifying the conformal covariance with the second gelfand dickey flow we covariantize moyal lax operators to construct the primary fields of one parameter deformation of classical w algebras

superconformally covariant operators and super w algebras superdifferential operators of order 2n 1 which are covariant with respect to superconformal changes of coordinates on a compact super riemann surface are studied herein it is shown that all such operators arise from super mobius covariant ones a canonical matrix representation is presented and applications to classical super w algebras are discussed

constructing soliton solutions and super bilinear form of lattice supersymmetric kdv equation the hirota bilinear form and multisoliton solution for semidiscrete and fully discrete difference difference versions of the supersymmetric korteweg de vries kdv equation found by xue et al 2013 j phys a math theor 46 502001 are presented the solitonic interaction term displays a fermionic dressing factor as in the continuous supersymmetric case using bilinear equations it is also shown that a new integrable semidiscrete and fully discrete version of supersymmetric kdv can be constructed with a simpler bilinear form but a more complicated interaction dressing its continuum limit is also computed

input output pseudolinearization for nonlinear systems an input output pseudolinearized system has the property that its family of linearizations about constant operating points has input output behavior that is independent of the operating point we develop a necessary and sufficient condition for existence of a state feedback and state coordinate change that transforms a given system into a pseudo normal form that is input output pseudolinearized these ideas are applied to obtain new approaches to approximate tracking and approximate inversion of nonlinear systems

a fully supersymmetric akns theory we construct a fully supersymmetric bihamiltonian theory in four superfields admitting zero curvature and lax formulation this theory is an extension of the classical akns which can be recovered as a reduction other supersymmetric theories are obtained as reductions of the susy akns namely a nonlinear schrodinger a modified kdv and the manin radul kdv the susy nonlinear schrodinger hierarchy is related to the one of roelofs and kersten we determine its bihamiltonian and lax formulation finally we show that the susy kdv s mentioned before are related through a susy miura map

quantized representation of some nonlinear integrable evolution equations on the soliton sector the hirota algorithm for solving several integrable nonlinear evolution equations is suggestive of a simple construction of a quantized representation of these equations and their soliton solutions over a fock space of bosons or of fermions the classical nonlinear wave equation becomes a nonlinear equation for an operator the solution of this equation is constructed through an operator analog of the hirota transformation the classical n soliton solution is the expectation value of the solution operator in an n particle state in the fock space the effect of perturbations that modify soliton identity is demonstrated

a new method for linearizing non linear systems the pseudolinearization consider the single input non linear system x f x u it has been shown that under mild conditions there exist transformations z t x v s x u such that in the z space the linear tangent model is independent of the operating point a constructive procedure to obtain the above transformations is described this new method is computationally attractive and effective in many practical cases

on the bihamiltonian structure of the supersymmetric kdv hierarchies a lie superalgebraic approach we give a lie superalgebraic interpretation of the bihamiltonian structure of known supersymmetric kdv equations we show that the loop algebra of a lie superalgebra carries a natural poisson pencil and we subsequently deduce the bihamiltonian structure of the supersymmetric kdv hierarchies by applying to loop superalgebras an appropriate reduction technique this construction can be regarded as a superextension of the drinfeld sokolov method for building a kdv type hierarchy from a simple lie algebra

approximate noninteracting control with stability for nonlinear systems a notion of approximate noninteracting control with stability for nonlinear systems is introduced and the design of both static and dynamic state feedback control laws that achieve this property for a given plant is considered this approach to the problem is based on the notion of extended linearization and begins with an extension of the linearization approach pointwise to all constant operating points in an open neighborhood of the nominal under natural assumptions it is shown that obstructions to extract noninteracting control with internal stability or input state output stability can be circumvented in the context of approximate noninteraction

quadratic conformal superalgebras abstract in this paper we shall classify quadratic conformal superalgebras by certain compatible pairs of a lie superalgebra and a novikov superalgebra four general constructions of such pairs are given moreover we shall classify such pairs related to simple novikov algebras

feedback control of nonlinear systems by extended linearization for single input multiple output nonlinear systems we consider a design method based on the family of linearizations of the system parameterized by constant operating points nonlinear state feedback control laws and observer state feedback control laws are designed such that the eigenvalues of the family of linearized closed loop systems are placed at specified values that are locally invariant with respect to the closed loop operating point the method is illustrated by application to the problem of automatically balancing an inverted pendulum

group invariant solutions for the n 2 super korteweg de vries equation the method of symmetry reduction is used to solve grassmann valued differential equations the n 2 supersymmetric korteweg de vries equation is considered it admits a lie superalgebra of symmetries of dimension 5 a two dimensional subsuperalgebra is chosen to reduce the number of independent variables in this equation we are then able to give different types of exact solutions in particular soliton solutions

supersymmetric extension of the korteweg de vries equation it is shown that among a one parameter family of supersymmetric extensions of the korteweg de vries equation there is a special system that has an infinite number of conservation laws which can be formulated in the second hamiltonian structure and which has a nontrivial lax representation its modified version is also discussed

on the gelfand dickey algebra gd sln and the wn symmetry i the bosonic case the algebra of nonlinear local and nonlocal differential operators acting on the ring of analytic functions is studied it is shown in particular that this space splits into 3 2 special subalgebras jr j 0 1 r 1 each subalgebra is completely specified by quantum numbers s and p q describing the conformal spin and the lowest and the highest degrees respectively the algebra and its dual of local pure nonlocal differential operators is used to calculate the general expression of the gelfand dickey bracket and the wn symmetry poisson one in terms of a set of spin j canonical fields uj 2 j n and a nonlinear u cubic dependent differential operator d n i j z u the explicit form of this operator is worked out other remarkable features are also discussed

approximate decoupling and asymptotic tracking for mimo systems this paper presents an algorithm for approximate input output decoupling of nonlinear mimo systems that are either numerically ill posed or exhibit nearly singular behavior in the application of decoupling algorithms although the systems considered are regular so that the exact decoupling algorithms are applicable in this case they require inversion of an ill conditioned matrix and yield high gain feedback solutions that may result in actuator saturation and cancellation of high frequency zeros the approximate algorithms of this paper are numerically robust and provide solutions that do not cancel far off right half plane zeros this latter characteristic is especially valuable when some of the far off right half plane zeros are unstable the algorithms are inspired by and are generalizations of some examples in the flight control literature

the zero curvature formulation of the skdv equations the fermionic extensions of the kdv equation are derived from the zero curvature condition associated with the superalgebra osp 2 1 this derivation clarifies why there are only two such extensions possible and why only one of them is supersymmetric a lenard type of derivation of these equations is also presented

rank invariants of nonlinear systems a linear algebraic framework for the analysis of rank properties of nonlinear systems is introduced this framework gives a high level interpretation of several existing algorithms built around the recursive computation of certain algebraic ranks associated with right invertibility left invertibility and dynamic decoupling furthermore it can be used to establish links between these algorithms and the differential algebraic approach as well as to solve some static and dynamic noninteracting control problems

bilinear approach to kuperschmidt super kdv type equations hirota bilinear form and soliton solutions for the super kdv korteweg de vries equation of kuperschmidt kuper kdv are given it is shown that even though the collision of supersolitons is more complicated than in the case of the supersymmetric kdv equation of manin radul the asymptotic effect of the interaction is simpler as a physical application it is shown that the well known fpu problem having a phonon mediated interaction of some internal degrees of freedom expressed through grassmann fields transforms to the kuper kdv equation in a multiple scale approach

the supersymmetric camassa holm equation and geodesic flow on the superconformal group we study a family of fermionic extensions of the camassa holm equation within this family we identify three interesting classes a equations which are inherently hamiltonian describing geodesic flow with respect to an h1 metric on the group of superconformal transformations in two dimensions b equations which are hamiltonian with respect to a different hamiltonian structure and c supersymmetric equations classes a and b have no intersection but the intersection of classes a and c gives a system with interesting integrability properties we demonstrate the painleve property for some simple but nontrivial reductions of this system and also discuss peakon type solutions

on darboux transformation of the supersymmetric sine gordon equation darboux transformation is constructed for superfields of the super sine gordon equation and the superfields of the associated linear problem the darboux transformation is shown to be related to the super backlund transformation and is further used to obtain n super soliton solutions

a new integrable equation valued on a cayley dickson algebra we introduce a new integrable equation valued on a cayley dickson c d algebra in the particular case in which the algebra reduces to a complex one the new interacting term in the equation cancels and the equation becomes the known korteweg de vries kdv equation for each c d algebra the equation has an infinite sequence of local conserved quantities we obtain a backlund transformation in the sense of walhquist estabrook for the equation for any cayley dickson algebra and relate it to a generalized gardner equation from this the infinite sequence of conserved quantities follows directly we give the explicit expression for the first few from the backlund transformation we get the lax pair and the one soliton and two soliton solutions generalizing the known solutions for the quaternion valued kdv equation from the gardner equation we obtain the generalized modified kdv equation which also has an infinite sequence of conserved quantities the new integrable equation is preserved under a subgroup of the automorphisms of the c d algebra in the particular case of the algebra of octonions the equation is invariant under

nonlinear quantum dynamical system based on the kadomtsev petviashvili ii equation the structure of soliton solutions of classical integrable nonlinear evolution equations which can be solved through the hirota transformation suggests a new way for the construction of nonlinear quantum dynamical systems that are based on the classical equations in the new approach the classical soliton solution is mapped into an operator u which is a nonlinear functional of the particle number operators over a fock space of quantum particles u obeys the evolution equation the classical soliton solutions are the eigenvalues of u in multi particle states in the fock space the construction easily allows for the incorporation of particle interactions which generate soliton effects that do not have a classical analog in this paper this new approach is applied to the case of the kadomtsev petviashvili ii equation the nonlinear quantum dynamical system describes a set of m 2s 1 particles with intrinsic spin s which interact in clusters of 1 n m 1 particles

analyticity of the srb measure of a lattice of coupled anosov diffeomorphisms of the torus we consider the thermodynamic limit of a d dimensional lattice of hyperbolic dynamical systems on the 2 torus interacting via weak and nearest neighbor coupling we prove that the srb measure is analytic in the strength of the coupling the proof is based on symbolic dynamics techniques that allow us to map the srb measure into a gibbs measure for a spin system on a d 1 dimensional lattice this gibbs measure can be studied by an extension decimation of the usual cluster expansion techniques

on the nature of the gardner transformation it is shown that every higher korteveg de vries equation can be included in a one parameter family of integrable equations

essential orders and the non linear decoupling problem abstract the concept of essential orders has recently been introduced into linear system theory and has been shown to be useful in the solution of static and dynamic decoupling problems commauit et al 1986 de luca et al 1985 this paper presents a non trivial extension to the class of non linear affine systems of some of these definitions and results it is shown that these invariant integers give the minimal order for a regular dynamic compensator that decouples a right invertible system

renormalization group and analyticity in one dimension a proof of dobrushin s theorem we consider one dimensional systems described by many body potentials with finite first moment and prove that the correlation functions are analytic in the interaction parameters this result is not new dobrushin 1973 but our proof is simpler and physically more transparent we show that by introducing suitable blocks and averaging over the variables associated to a subset of the blocks decimation procedure the resulting effective interaction is such that the system can always be dealt with as a high temperature system

uniqueness and exponential decay of correlations for some two dimensional spin lattice systems we consider a two dimensional lattice spin system which naturally arises in dynamical systems called coupled map lattice the configuration space of the spin system is a direct product of mixing subshifts of finite type the potential is defined on the set of all squares in z2 and decays exponentially with the linear size of the square via the polymer expansion technique we prove that for sufficiently high temperatures the limit gibbs distribution is unique and has an exponential decay of correlations

dressing operator approach to the toroidal model of higher dimensional dispersionless kp hierarchy based upon the dressing operator approach we investigate the twistor theoretical construction additional symmetries hodograph solutions and miura transformation for the toroidal model of higher dimensional dispersionless kp hierarchy introduced by takasaki

polymer gas approach to n body lattice systems we give a simple proof based only on combinatorial arguments of the koteck preiss condition for the convergence of the cluster expansion then we consider spin systems with long range n body interactions we prove directly using the polymer gas representation that the pressure may be written in terms of an absolutely convergent series uniformly in the volume when the interaction is summable in a suitable sense we also give an estimate of this radius of convergence in order to get the proof we use a method introduced by cassandro and olivieri in the early 1980s we apply this method to various concrete examples

linear response function for coupled hyperbolic attractors the srb measures of a hyperbolic system are widely accepted as the measures that are physically relevant it has been shown by ruelle that they depend smoothly on the system furthermore ruelle showed by a separate argument that the first derivative i e the linear response function admits a geometric interpretation in this paper we consider thermodynamic limits of srb measures in lattices of coupled hyperbolic attractors in a previous paper using markov partitions and thermodynamic formalism we had established the smooth dependence of thermodynamic limits of srb measures here we establish that the linear response function admits a geometric interpretation the formula is analogous to the one found by ruelle for finite dimensional systems if one term is reinterpreted appropriately we show that the limiting derivative is the thermodynamic limit of the derivatives in finite volume we also obtain similar results for the derivatives of the entropy

a local fluctuation theorem abstract a mechanism for the validity of a local version of the fluctuation theorem uniform in the system size is discussed for a reversible chain of weakly coupled anosov systems

fermionic covariant prolongation structure theory for multidimensional super nonlinear evolution equation the fermionic covariant prolongation structure theory is investigated we extend the fermionic covariant prolongation structure technique to the multidimensional super nonlinear evolution equation and present the fermionic covariant fundamental equations determining the prolongation structure furthermore we investigate a 2 1 dimensional super nonlinear schrodinger equation and analyze its integrability by means of this prolongation structure technique we derive its lax representation and backlund transformation moreover we present a solution of this multidimensional super integrable equation

bilinearization of n 1 supersymmetric korteweg de vries equation revisited we consider the n 1 supersymmetric korteweg de vries skdv equation within the framework of hirota s bilinear method we construct a backlund transformation which may be interpreted as the modified skdv equation also we find a lax representation and a nonlinear superposition formula by direct applications of the nonlinear superposition formula we calculate soliton solutions for the skdv equation

symmetries of supersymmetric integrable hierarchies of kp type this article is devoted to the systematic study of additional non isospectral symmetries of constrained reduced supersymmetric integrable hierarchies of kp type the so called skp r mb mf models the latter are supersymmetric extensions of ordinary constrained kp hierarchies which contain as special cases basic integrable systems such as m kdv akns fordy kulish yajima oikawa etc as a first main result it is shown that any skp r mb mf hierarchy possesses two different mutually anti commuting types of superloop superalgebra additional symmetries corresponding to the positive and negative grade parts of certain superloop superalgebras the second main result is the systematic construction of the full algebra of additional virasoro symmetries of skp r mb mf hierarchies which requires nontrivial modifications of the virasoro flows known from the general case of unconstrained manin radul super kp hierarchies the latter flows do not define symmetries for constrained skp r mb mf hierarchies as

the painleve analysis for n 2 super korteweg de vries equations the painleve analysis of a generic multiparameter n 2 extension of the korteweg de vries kdv equation is presented unusual aspects of the analysis pertaining to the presence of two fermionic fields are emphasized for the general class of models considered we find that the only ones which manifestly pass the test are precisely the four known integrable supersymmetric kdv equations including the skdv1 case

supersymmetric reciprocal transformation and its applications the supersymmetric analog of the reciprocal transformation is introduced this is used to establish a transformation between one of the supersymmetric harry dym equations and the supersymmetric modified korteweg de vries equation the reciprocal transformation as a backlund type transformation between these two equations is adopted to construct a recursion operator for the supersymmetric harry dym equation by proper factorization of the recursion operator a bi hamiltonian structure is found for the supersymmetric harry dym equation furthermore a supersymmetric kawamoto equation is proposed and is associated with the supersymmetric sawada kotera equation the recursion operator and odd bi hamiltonian structure of the supersymmetric kawamoto equation are also constructed

a supertrace identity and its applications to superintegrable systems a supertrace identity on lie superalgebras is established it provides a tool for constructing super hamiltonian structures of zero curvature equations associated with lie superalgebras applications in the case of the lie superalgebra b 0 1 present super hamiltonian structures of a super akns soliton hierarchy and a super dirac soliton hierarchy

n 4 super kdv hierarchy in n 4 and n 2 superspaces we present the results of further analysis of the integrability properties of the n 4 supersymmetric korteweg de vries kdv equation deduced earlier by two of us f delduc and e ivanov phys lett b 309 312 1993 as a hamiltonian flow on n 4 su 2 superconformal algebra in the harmonic n 4 superspace to make this equation and the relevant hamiltonian structures more tractable we reformulate it in the ordinary n 4 and further in n 2 superspaces in n 2 superspace it is represented by a coupled system of evolution equations for a general n 2 superfield and two chiral and antichiral superfields and involves two independent real parameters a and b we construct a few first bosonic conserved charges in involution of dimensions from 1 to 6 and show that they exist only for the following choices of the parameters i a 4 b 0 ii a 2 b 6 iii a 2 b 6 the same values are needed for the relevant evolution equations including n 4 kdv itself to be bi hamiltonian we demonstrate that the above three options are related via su 2 transformations and actually amount to the su 2 covariant integrability condition found in the harmonic superspace approach our results provide a strong evidence that the unique n 4 su 2 super kdv hierarchy exists upon reduction to n 2 kdv the above three possibilities cease to be equivalent they give rise to the a 4 and a 2 n 2 kdv hierarchies which thus prove to be different truncations of the single n 4 su 2 kdv one

approximation by regular input output maps the authors study approximate dynamic input output linearization in the sense of j hauser et al 1989 for multiinput multioutput mimo nonlinear systems which exhibit singularities in the dynamic extension process

on the bi hamiltonian structures of the skdv the first and the second hamiltonian structures of the supersymmetric kdv equation are derived following the conventional approach of gel fand and dickey in particular it is shown that the nonlocal nature of the first bracket is a direct consequence of the constrained nature of the lax operator

smooth dependence of thermodynamic limits of srb measures the thermodynamic limits of srb measures for uniformly hyperbolic sets are smoothly dependent on the map in an appropriate functional space

prolongation structures for supersymmetric equations the well known prolongation technique of wahlquist and estabrook 1975 for nonlinear evolution equations is generalized for supersymmetric equations and applied to the supersymmetric extension of the kdv equation of manin radul using the theory of kac moody lie superalgebras the explicit form of the resulting lie superalgebra is determined it is shown to be isomorphic to rmr cov c 2 sigma where rmr is an eight dimensional radical an auto backlund transformation is derived from the prolongation structure and the relationship with known solution methods of the skdv equation is analysed in addition it is indicated how a super position principle for the skdv equation can be obtained

supersymmetric moyal lax representation the super moyal lax representation and the super moyal momentum algebra are introduced and the properties of simple and extended supersymmetric integrable models are systematically investigated it is shown that much like in the bosonic cases the super moyal lax equation can be interpreted as a hamiltonian equation and can be derived from an action similarly we show that the parameter of non commutativity in this case is related to the central charge of the second hamiltonian structure of the system the super moyal lax description allows us to go to the dispersionless limit of these models in a singular limit and we discuss some of the properties of such systems

diffusion in energy conserving coupled maps we consider a dynamical system consisting of subsystems indexed by a lattice each subsystem has one conserved degree of freedom energy the rest being uniformly hyperbolic the subsystems are weakly coupled together so that the sum of the subsystem energies remains conserved we prove that the subsystem energies satisfy the diffusion equation in a suitable scaling limit

a bosonization procedure for hamiltonian theories with fermions hamiltonian theories with fermions are proved to be equivalent to hierarchies of ordinary hamiltonian theories the corresponding poisson brackets are defined in terms of the original super poisson structure while hamiltonian functions are simply the coefficients in the expansion of the super hamiltonian function as a formal power series in grassman generators fermion extensions of the kdv equation are considered to illustrate the general result its space supersymmetric extensions are used to show in particular how supersymmetry transformations can be recast as ordinary hamiltonian symmetries

on the integrability of the super kdv equation supersymmetric analogues of the gelfand dikii polynomials are derived an alternative proof of the super kdv equation is given using identities obeyed by the polynomials they also allow the recursive generation of the infinite number of conserved quantities for the super kdv flow

the bi hamiltonian structure of fully supersymmetric korteweg de vries systems the bi hamiltonian structure of integrable supersymmetric extensions of the korteweg de vries kdv equation related to then 1 and then 2 superconformal algebras is found it turns out that some of these extensions admit inverse hamiltonian formulations in terms of presymplectic operators rather than in terms of poisson tensors for one extension related to then 2 case additional symmtries are found with bosonic parts that cannot be reduced to symmetries of the classical kdv they can be explained by a factorization of the corresponding lax operator all the bi hamiltonian formulations are derived in a systematic way from the lax operators

a supersymmetric extension of the kadomtsev petviashvili hierarchy an extension of the kadomtsev petviashvili hierarchy by odd variables is given conservation laws and formal integrability are proved

approximate linearization by state feedback and coordinate change a nonlinear system can always be approximated to first order by linear systems it has been shown by jakubczyk and respondek 4 and hunt and su 3 that certain nonlinear systems are the exact transforms of linear systems under nonlinear state coordinate change and nonlinear state feedback in this paper we give necessary and sufficient conditions for a nonlinear system to be approximated to higher order by the transform of a linear system the use of this technique in the design of nonlinear compensators has been suggested recently by the author 6

almost disturbance decoupling for single input single output nonlinear systems the almost disturbance decoupling problem for nonlinear single input single output systems is addressed by using singular perturbation methods and high gain feedback sufficient conditions and the explicit high gain nonlinear state feedback in solvable cases are given they generalize both previous almost results for linear systems and exact ones for nonlinear systems the necessity of the conditions is discussed in particular an example is given where the main structural condition is not satisfied and the high gain control designed on the basis of linear approximations fails to achieve almost disturbance decoupling for the original system

integrable system constructed out of two interacting superconformal fields we consider an interaction between superconformal fields of the same gradation this entails the construction of a supersymmetric poisson tensor for these fields generating a new class of hamiltonian systems the lax representation is found for one of them by supersymmetrizing the lax operator for the hirota satsuma equation the supersymmetric equation is not reducible to the classical hirota satsuma case we show that our generalized system can be reduced to the the supersymmetric kdv equation a 4 surprisingly the integrals of motion are not reduced to integrals of motion of the supersymmetric kdv equation

supersymmetric version of a hydrodynamic system in riemann invariants and its solutions in this paper a supersymmetric extension of a system of hydrodynamic type equations involving riemann invariants is formulated in terms of a superspace and superfield formalism the symmetry properties of both the classical and supersymmetric versions of this hydrodynamical model are analyzed through the use of group theoretical methods applied to partial differential equations involving both bosonic and fermionic variables more specifically we compute the lie superalgebras of both models and perform classifications of their respective subalgebras a systematic use of the subalgebra structures allows us to construct several classes of invariant solutions including traveling waves centered waves and solutions involving monomials exponentials and radicals

riemann liouville integrals of fractional order and extended kp hierarchy an attempt to formulate the extensions of the kp hierarchy by introducing fractional order pseudo differential operators is given in the case of the extension with the half order pseudo differential operators a system analogous to the supersymmetric extensions of the kp hierarchy is obtained unlike the supersymmetric extensions no grassmannian variable appears in the hierarchy considered here more general hierarchies constructed by the 1 nth order pseudo differential operators their integrability and the reduction procedure are also investigated in addition to finding the new extensions of the kp hierarchy a brief introduction to the riemann liouville integral is provided to yield a candidate for the fractional order pseudo differential operators

an operator valued extension of the super korteweg de vries equations an extension of the super korteweg de vries kdv integrable system in terms of operator valued functions is obtained following the ideas of gardner a general algebraic approach for finding the infinitely many conserved quantities of integrable systems is presented the approach is applied to the above described system and infinitely many conserved quantities are constructed in a particular case they reduce to the corresponding conserved quantities of super kdv

integrable fermionic extensions of the garnier system and the anharmonic oscillator we first derive a fermionic extension of the garnier system by applying the method of binary nonlinearization of spectral problem to the supersymmetric kdv equation of kupershmidt and then a fermionic extension of the anharmonic oscillator by a simple reduction the integrable properties of resulting systems such as lax representations corresponding r matrices and conversed integrals of motion are established

super loop groups hamiltonian actions and super virasoro algebras the quotient widetilde lg mathord left vphantom widetilde lg g right kern nulldelimiterspace g of a super loop group widetilde lg by the subgroup of constant loops is given a supersymplectic structure and identified through a moment map embedding open image in new window with a coadjoint orbit of the centrally extended super loop algebra open image in new window the algebra widetilde diff c s 1 of super conformal vector fields on the circle is shown to have a natural representation as hamiltonian vector fields on widetilde lg mathord left vphantom widetilde lg g right kern nulldelimiterspace g generated by an equivariant moment map open image in new window this map is obtained by composition of315 8 with a super poisson map open image in new window defining a supersymmetric extension of the classical sugawara formula upon quantization this yields the corresponding formula of kac and todorov on unitary highest weight representations for any homomorphism u 1 g an associated twisted moment map open image in new window is also derived generating a super poisson bracket realization of a super virasoro subalgebra widetilde vir of the semi direct sum open image in new window the corresponding super poisson map open image in new window is interpreted as a nonabelian generalization of the super miura map and applied to two super kdv hierarchies to derive corresponding integrable generalized super mkdv hierarchies in open image in new window

quasi periodic waves of the n 1 supersymmetric modified korteweg de vries equation abstract based on the hirota bilinear method and the riemann theta function a straightforward way is shown to construct quasi periodic wave solutions of supersymmetric equations the resulting theory is applied to the supersymmetric modified korteweg de vries equation further we analyze the asymptotic properties of the solutions and give their asymptotic relations between the quasi periodic wave solutions and the soliton solutions

infinite dimensional srb measures we review the basic steps leading to the construction of a sinai ruelle bowen srb measure for an infinite lattice of weakly coupled expanding circle maps and we show that this measure has exponential decay of space time correlations first using the perron frobenius operator one connects the dynamical system of coupled maps on a d dimensional lattice to an equilibrium statistical mechanical model on a lattice of dimension d 1 this lattice model is for weakly coupled maps in a high temperature phase and we use a general but very elementary method to prove exponential decay of correlations at high temperatures

supersymmetric extensions of the harry dym hierarchy we study the supersymmetric extensions of the harry dym hierarchy of equations we obtain the susy b extension the doubly susy b extension as well as the n 1 and the n 2 supersymmetric extensions for this system the n 2 supersymmetric extension is particularly interesting since it leads to new classical integrable systems in the bosonic limit we prove the integrability of these systems through the bi hamiltonian formulation of integrable models and through the lax description we also discuss the supersymmetric extension of the hunter zheng equation which belongs to the harry dym hierarchy of equations

necessary conditions for asymptotic tracking in nonlinear systems in the literature it has been shown that if a single input single output analytic nonlinear plant 1 has a well defined relative degree and 2 is minimum phase it is possible to achieve asymptotic tracking for an open set of output trajectories containing the origin in c sup n 0 spl infin the space of n times continuously differentiable functions taking values in r when either of these sufficient conditions is not met various authors have investigated approximate analytic solutions discontinuous solutions and solutions for restricted sets of trajectories in this paper it is shown that conditions 1 and 2 are necessary for the existence of an analytic compensator which yields asymptotic tracking for an open set of output trajectories analogous results are established for multi input multi output systems

the fully supersymmetric akns equations the general fully supersymmetric approach to the akns method is presented the supersymmetric kdv and mkdv equations are considered as examples the supersymmetric backlund transformation is constructed for the supersymmetric kdv equation

equilibrium measures for coupled map lattices existence uniqueness and finite dimensional approximations we consider coupled map lattices of hyperbolic type i e chains of weakly interacting hyperbolic sets attractors over multi dimensional lattices we describe the thermodynamic formalism of the underlying spin lattice system and then prove existence uniqueness mixing properties and exponential decay of correlations of equilibrium measures for a class of holder continuous potential functions with a sufficiently small holder constant we also study finite dimensional approximations of equilibrium measures in terms of lattice systems approximations and lattice spin systems d approximations we apply our results to establish existence uniqueness and mixing property of srb measures as well as obtain the entropy formula

a new n 2 supersymmetric korteweg de vries equation there are two known integrable n 2 space supersymmetric extensions of the kdv equation both can be written as hamiltonian systems with a common poisson structure which corresponds to the n 2 supersymmetric form of the second kdv structure by analyzing the conservation laws of the one parameter family of equations that share this hamiltonian structure one finds that a third system is singled out by the existence of nontrivial conservation laws it is conjectured to be integrable

analyticity of the sinai ruelle bowen measure for a class of simple anosov flows we consider perturbations of the hamiltonian flow associated with the geodesic flow on a surface with constant negative curvature we prove that under a small perturbation not necessarily of hamiltonian character the sinai ruelle bowen measure associated with the flow exists and is analytic in the strength of the perturbation an explicit example of thermostated dissipative dynamics is considered

supersymmetric extension of the scalar born infeld equation in this paper a supersymmetric extension of the scalar born infeld equation is constructed through a superspace formalism which involves the addition of one independent fermionic grassmann variable to the existing bosonic spacetime coordinates the bosonic scalar field is replaced by a fermionic superfield which is composed of two component fields one bosonic and one fermionic the resulting equation is invariant under a space supersymmetric transformation and in its most general form involves four arbitrary parameters for a certain specific case the lie superalgebra of symmetries was identified and the one dimensional subalgebras were systematically classified into splitting and non splitting conjugate classes a number of group invariant solutions were obtained including polynomial solutions solutions by radicals and solitary waves including bumps kinks and doubly periodic solutions

on n 3 super korteweg de vries equation a one parameter family is constructed of n 3 supersymmetric and so 3 symmetric extensions of the korteweg de vries kdv equation as a hamiltonian flow on a n 3 superconformal algebra and it is argued that it is nonintegrable for any choice of the parameter then a modified n 3 super kdv equation is proposed which possesses the higher order conserved quantities and so is a candidate for an integrable system upon reduction to n 2 it yields the recently discussed would be integrable version of the n 2 super kdv equation in the bosonic core it contains a coupled system of the kdv type equation and a three component generalization of the mkdv equation a hamiltonian formulation of the new n 3 super kdv equation as a flow on some contraction of the direct sum of two n 3 superconformal algebras is given

higher order approximate feedback linearization about a manifold for multi input systems considers the problem of approximately feedback linearizing a multi input nonlinear system around the equilibrium manifold spl epsi while making the error terms be of highest order on spl epsi necessary and sufficient conditions are given for approximately feedback linearizing the system around spl epsi with error terms of order spl rho on spl epsi a simple multi input example is given to illustrate the higher order approximate feedback linearization procedure

a geometrical formulation of fermionic integrable systems a fermionic hamiltonian system is formulated on a supermanifold it is shown that if the system possesses a bi hamiltonian structure one can naturally define a lax equation associated with a 1 1 tensor on this supermanifold and this allows one to construct a set of conserved quantities furthermore if the corresponding nijenhuis tensor vanishes it is shown that all these conserved quantities would be in involution which is a sufficient condition for integrability of the system the fermionic extension of the kdv equation with a bi hamiltonian structure within this geometrical approach is studied

a supersymmetric version of a gaussian irrotational compressible fluid flow the lie point symmetries and corresponding invariant solutions are obtained for a gaussian irrotational compressible fluid flow a supersymmetric extension of this model is then formulated through the use of a superspace and superfield formalism the lie superalgebra of this extended model is determined and a classification of its subalgebras is performed the method of symmetry reduction is systematically applied in order to derive special classes of invariant solutions of the supersymmetric model several new types of algebraic hyperbolic multi solitonic and doubly periodic solutions are obtained in explicit form

dynamic decoupling for right invertible nonlinear systems abstract it is shown that every system with more inputs than outputs that is right invertible in the sense of 5 can be decoupled via a dynamic state feedback that can be computed using a given algorithm this result generalizes the one of 2 and completes the results of 3

lax equation lie algebra automorphism and nonlinear supersymmetric dynamical systems following an idea of bogoyavlensky 1988 it is shown that a nonlinear supersymmetric integrable system can be constructed by using the automorphisms of supersymmetric lie algebra

two super camassa holm equations reciprocal transformations and applications reciprocal transformations are introduced for two super camassa holm ch equations under these transformations and appropriate changes of dependent variables the super ch equation proposed by geng et al stud appl math 130 1 2013 is converted to a negative member of the super korteweg de vries kdv hierarchy studied by geng and wu in 2010 appl math lett 23 716 2010 while the other super ch equation due to zhang and zuo j math phys 52 073503 2011 is related to a new super kdv hierarchy in the latter case algebraic properties of this new super kdv hierarchy are established including hamiltonian operators a recursion operator and conserved quantities

invariant solutions of supersymmetric nonlinear wave equations systematic group theoretical analyses of two supersymmetric nonlinear wave equations namely the supersymmetric sinh gordon and polynomial klein gordon equations are performed in each case a generalization of the method of prolongations is used to determine the lie superalgebra of symmetries and the method of symmetry reduction is applied in order to obtain invariant solutions of the supersymmetric equations under consideration in the case of the supersymmetric sinh gordon equation the results are compared with those previously found for the supersymmetric sine gordon equation the presence of non standard invariants is discussed for the supersymmetric sinh gordon and polynomial klein gordon equations

supersymmetric extensions of the nonlinear schrodinger equation symmetries and coverings a construction is proposed for a supersymmetric generalization of the cubic schrodinger equation resulting in two supersymmetric systems one of which contains a free parameter both systems are proven to admit an infinite set of higher order local and nonlocal symmetries and a seemingly infinite set of conservation laws the lowest order terms of which are given explicitly moreover the theory of coverings equivalent to the prolongation method of wahlquist and estabrook is applied to both systems both are seen to admit an infinite dimensional covering algebra the structure of which is determined explicitly resulting in a related supersymmetric system of differential equations as well as an auto backlund transformation for each equation this indicates the complete integrability of both systems

a note on the invertibility of nonlinear input output differential systems abstract a new conceptual framework employing differential algebra is proposed for solving the long standing problem of inverting nonlinear input output differential systems simple characterizations of left and right invertibility are given which rest upon an invariant integer which for constant linear systems turns out to be the rank of the transfer matrix

variational calculus of supervariables and related algebraic structures abstract we establish a formal variational calculus of supervariables which is a combination of the bosonic theory of gel fand dikii and the fermionic theory in our earlier work certain interesting new algebraic structures are found in connection with hamiltonian superoperators in terms of our theory in particular we find connections between hamiltonian superoperators and novikov poisson algebras that we introduced in our earlier work in order to establish a tensor theory of novikov algebras furthermore we prove that an odd linear hamiltonian superoperator in our variational calculus induces a lie superalgebra which is a natural generalization of the super virasoro algebra under certain conditions

integrable hierarchies related to the kuper ch spectral problem in this paper from a given kuper ch spectral problem we propose two kinds of super integrable hierarchies one is the kuper ch hierarchy the other is the generalized kuper harry dym hierarchy moreover we construct their zero curvature representations and super bi hamiltonian structures

multi component bi super hamiltonian kdv systems it is shown that a new class of classical multi component super kdv equations is bi super hamiltonian by extending the method for the verification of graded jacobi identity the multi component extension of super mkdv equations is obtained by using the super miura transformation