matrix kadomtsev petviashvili equation matrix identities and explicit non singular solutions a new version of the backlund darboux transformation for the matrix kadomtsev petviashvili kp equation is used to construct and study explicit multi parameter solutions and wavefunctions in terms of the matrix exponents a class of the self adjoint non singular solutions of kp i is introduced using the controllability notion from the system theory a subclass of the rationally decaying self adjoint non singular solutions is studied in particular several results prove new in the scalar case also

einstein maxwell solitons the application of the inverse scattering method to the einstein maxwell equations for stationary axisymmetric exterior fields leads the authors to an explicit formula for the ernst and electromagnetic potentials of new exact solutions generated from an arbitrary seed solution

equivalence of various pseudopotential approaches for einstein maxwell fields in the literature various systems of liner eigenvalue equations from which the einstein maxwell equations for stationary axisymmetric exterior fields follow as the integrability conditions were derived in the present paper these linear systems are shown to be equivalent the explicit transformations mapping one form to another are given

multiple travelling wave solutions of nonlinear evolution equations using a unified algebraic method a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system compared with most of the existing tanh methods the jacobi elliptic function method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the travelling wave solutions according to the values of some parameters the solutions obtained in this paper include a kink shaped and bell shaped soliton solutions b rational solutions c triangular periodic solutions and d jacobi and weierstrass doubly periodic wave solutions among them the jacobi elliptic periodic wave solutions exactly degenerate to the soliton solutions at a certain limit condition the efficiency of the method can be demonstrated on a large variety of nonlinear evolution equations such as those considered in this paper kdv mkdv ito s fifth mkdv hirota nizhnik novikov veselov broer kaup generalized coupled hirota satsuma coupled schrodinger kdv 2 1 dimensional dispersive long wave 2 1 dimensional davey stewartson equations in addition as an illustrative sample the properties of the soliton solutions and jacobi doubly periodic solutions for the hirota equation are shown by some figures the links among our proposed method the tanh method extended tanh method and the jacobi elliptic function method are clarified generally

darboux transformations and exact solutions of two dimensional c 1 l and d 2 l 1 toda equations for the two dimensional toda equations corresponding to the kac moody algebras c 1 l and d 2 l 1 the darboux transformations which keep all the reductions of the lax pairs are constructed the lowest degrees of the darboux transformations are 2l 2 for c 1 l and 2l for d 2 l 1 exact solutions of these toda equations are presented in a purely algebraic way

response probability distribution of built up vibro acoustic systems the vibro acoustic response of built up structures consisting of stiff components with low modal density and flexible components with high modal density is sensitive to small imperfections in the flexible components in this paper the uncertainty of the response is considered by modeling the low modal density master system as deterministic and the high modal density subsystems in a nonparametric stochastic way i e carrying a diffuse wave field and by subsequently computing the response probability density function the master system s mean squared response amplitude follows a singular noncentral complex wishart distribution conditional on the subsystem energies for a single degree of freedom this is equivalent to a chi square or an exponential distribution depending on the loading conditions the subsystem energies follow approximately a chi square distribution when their relative variance is smaller than unity the results are validated by application to plate structures and good agreement with monte carlo simulations is found

a generalized formula for integrable classes of surfaces in lie algebras we discuss relations between the approach of fokas and gelfand to immersions on lie algebras and the theory of soliton surfaces of sym we show that many results concerning immersions on lie algebras can be reduced to or interpreted within the soliton surfaces approach we present also some new results including a generalization of the fokas gelfand formula for integrable classes of surfaces in lie algebras and in particular in pseudo euclidean n dim spaces the generalized formula is used to formulate a method of constructing integrable classes of surfaces as an example we discuss the class of linear weingarten surfaces defined by the linear relationship between gaussian and mean curvatures we construct explicitly a one parameter family of linear weingarten surfaces parallel equidistant to a given pseudospherical surface

solitary wave and periodic wave solutions for the thermally forced gravity waves in atmosphere by introducing a new transformation a new direct and unified algebraic method for constructing multiple travelling wave solutions of general nonlinear evolution equations is presented and implemented in a computer algebraic system which extends fan s direct algebraic method to the case when r 4 the solutions of a first order nonlinear ordinary differential equation with a higher degree nonlinear term and fan s direct algebraic method of obtaining exact solutions to nonlinear partial differential equations are applied to the combined kdv mkdv gkdv equation which is derived from a simple incompressible non hydrostatic boussinesq equation with the influence of thermal forcing and is applied to investigate internal gravity waves in the atmosphere as a result by taking advantage of the new first order nonlinear ordinary differential equation with a fifth degree nonlinear term and an eighth degree nonlinear term periodic wave solutions associated with the jacobin elliptic function and the bell and kink profile solitary wave solutions are obtained under the effect of thermal forcing most importantly the mechanism of propagation and generation of the periodic waves and the solitary waves is analysed in detail according to the values of the heating parameter which show that the effect of heating in atmosphere helps to excite westerly or easterly propagating periodic internal gravity waves and internal solitary waves in atmosphere which are affected by the local excitation structures in atmosphere in addition as an illustrative sample the properties of the solitary wave solution and jacobin periodic solution are shown by some figures under the consideration of heating interaction

on the applicability of the lognormal distribution in random dynamical systems this paper is concerned with the probability density function of the energy of a random dynamical system subjected to harmonic excitation it is shown that if the natural frequencies and mode shapes of the system conform to the gaussian orthogonal ensemble then under common types of loading the distribution of the energy of the response is approximately lognormal providing the modal overlap factor is high typically greater than two in contrast it is shown that the response of a system with poisson natural frequencies is not approximately lognormal numerical simulations are conducted on a plate system to validate the theoretical findings and good agreement is obtained simulations are also conducted on a system made from two plates connected with rotational springs to demonstrate that the theoretical findings can be extended to a built up system the work provides a theoretical justification of the commonly used empirical practice of assuming that the energy response of a random system is lognormal

a fully polynomial approximation scheme for the weighted earliness tardiness problem a fully polynomial approximation scheme for the problem of scheduling n jobs on a single machine to minimize total weighted earliness and tardiness is presented a new technique is used to develop the scheme the main feature of this technique is that it recursively computes lower and upper bounds on the value of partial optimal solutions therefore the scheme does not require any prior knowledge of lower and upper bounds on the value of a complete optimal solution this distinguishes it from all the existing approximation schemes

binormal motion of curves of constant curvature and torsion generation of soliton surfaces the purely binormal motion of curves of constant curvature or torsion respectively is shown to lead to integrable extensions of the dym and classical sine gordon equations in the case of the extended dym equation a reciprocal invariance is used to establish the existence of novel dual soliton surfaces associated with a given soliton surface a cc ideal formulation is adduced to obtain a matrix darboux invariance for the extended dym and reciprocally linked m 2 kdv equations a backlund transformation with a classical constant length property is thereby constructed which allows the generation of associated soliton surfaces analogues of both backlund9s and bianchi9s classical transformations are derived for the extended sine gordon system

pseudospherical surfaces on time scales a geometric definition and the spectral approach we define and discuss the notion of pseudospherical surfaces in asymptotic coordinates on time scales thus we extend well known notions of discrete pseudospherical surfaces and smooth pseudosperical surfaces on more exotic domains e g the cantor set in particular we present a new expression for the discrete gaussian curvature which turns out to be valid for asymptotic nets on any time scale we show that asymptotic chebyshev nets on an arbitrary time scale have constant negative gaussian curvature we present also the quaternion valued spectral problem the lax pair and the darboux backlund transformation for pseudospherical surfaces in asymptotic coordinates on arbitrary time scales

on the geometry of the inhomogeneous heisenberg ferromagnet nonintegrable case new classes of exact solutions of the inhomogeneous heisenberg ferromagnet equation are found by means of a geometrical technique this technique consists of calculating one parameter families of geodesics on surfaces in e3 the solutions correspond to geodesics on surfaces of rotation

darboux transformation and soliton like solutions for the gerdjikov ivanov equation an explicit n fold darboux transformation with multiparameters for a kind of coupled derivative nonlinear schrodinger equation is constructed with the help of a gauge transformation of a spectral problem as a reduction a darboux transformation of the gerdjikov ivanov equation is obtained furthermore the explicit soliton like solutions of the gerdjikov ivanov equation are given by applying its darboux transformation

on integrability of the inhomogeneous heisenberg ferromagnet model examination of a new test we present an improved version of the integrability test based on application of lie point transformations acting on the bare linear problem the test is then applied to the inhomogeneous heisenberg ferromagnet model equation the integrable cases selected by this test are identical with those obtained by the standard painleve test

single machine scheduling with release dates and rejection abstract in this paper we consider the single machine scheduling problem with release dates and rejection a job is either rejected in which case a rejection penalty has to be paid or accepted and processed on the machine the objective is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs we show that the problem is np hard in the ordinary sense then we provide two pseudo polynomial time algorithms consequently two special cases can be solved in polynomial time finally a 2 approximation algorithm and a fully polynomial time approximation scheme are given for the problem

prolongation structures for harry dym type equations and backlund transformations of cc ideals the authors examine the prolongation structures for a certain class of differential equations the interrelation between the incomplete set of commutator relations and the defining relations for kac moody algebras is discussed constant coefficient ideals are introduced for which backlund transformations are found in a purely algebraic manner

accurate extreme value based frequency response bounding for structures with a small number of highly random parameters abstract a modified extreme value based methodology is discussed for computing statistical bounds associated with the magnitude of the frequency response of a specified number of structures with high levels of random parameter uncertainty the methodology intended for small numbers of uncertain parameters is capable of constructing accurate statistical bounds in terms of quantiles associated with the extreme value distribution quantiles can be constructed for an ensemble of structural responses across the entire frequency range without using monte carlo simulation to test the methodology statistical bounds for the energy of an l shaped structure with low and high levels of uniformly distributed length and thickness variability are obtained i via direct integration using an ansys finite element model and ii via statistical energy analysis sea comparisons are shown with bounds obtained using monte carlo simulation the merit of direct integration for computing bounds associated with the responses of an ensemble of structures with high levels of random parameter uncertainty is demonstrated by its simplicity high accuracy and absence of statistical scatter

parallel machine scheduling with deteriorating jobs rejection and a fixed non availability interval we consider two parallel machine scheduling problem in which the processing time of a job is a simple linear increasing function of its starting time jobs can be rejected by paying penalties and the first machine has a fixed non availability interval the objective is to minimize the makespan of the accepted jobs plus the total penalty of the rejected jobs we present a fully polynomial time approximation scheme fptas for the case with two identical machines the time complexity of the fptas is o n 6l 4 e 3 where n is the number of jobs and l is the input size e is the error bound

darboux transformations finite reduction groups and related yang baxter maps in this paper we construct yang baxter yb maps using darboux matrices which are invariant under the action of finite reduction groups we present six dimensional yb maps corresponding to darboux transformations for the nonlinear schrodinger nls equation and the derivative nonlinear schrodinger dnls equation these yb maps can be restricted to four dimensional yb maps on invariant leaves the former are completely integrable and they also have applications to a recent theory of maps preserving functions with symmetries fordy a and kassotakis a 2013 j phys a math theor 46 205201 we give a six dimensional yb map corresponding to the darboux transformation for a deformation of the dnls equation we also consider vector generalizations of the yb maps corresponding to the nls and dnls equations

quasideterminant solutions of the generalized heisenberg magnet model in this paper we present the darboux transformation for the generalized heisenberg magnet ghm model based on the general linear lie group gl n and construct multi soliton solutions in terms of quasideterminants further we relate the quasideterminant multi soliton solutions obtained by means of darboux transformation with those obtained by the dressing method we also discuss the model based on the lie group su n and obtain explicit soliton solutions of the model based on su 2

a new approach to the darboux backlund transformation versus the standard dressing method we present a new approach to the construction of the darboux matrix this is a generalization of a recently formulated method based on the assumption that the square of the darboux matrix vanishes for some values of the spectral parameter we consider the multisoliton case the reduction problem and the discrete case the relationships between our approach the zakharov shabat dressing method and the neugebauer meinel method are discussed in detail

backlund transformations for the un pumped maxwell bloch system and the fifth painleve equation a backlund transformation for the un pumped maxwell bloch system governing phenomena in nonlinear optics is derived the approach is based on the use of constant coefficient ideals cc ideals since the maxwell bloch system in a certain one dimensional reduction is connected to the fifth painleve equation via a contact transformation chains of solutions for the latter equation are obtained as illustration some rational solutions are explicitly given

darboux covariant equations of von neumann type and their generalizations lax pairs with operator valued coefficients which are explicitly connected by means of an additional condition are considered this condition is proved to be covariant with respect to the darboux transformation of a general form nonlinear equations arising from the compatibility condition of the lax pairs in the matrix case include in particular nahm equations and volterra bogoyavlenskii and toda lattices the examples of other one two and multi field lattice equations are also presented

an efficient probabilistic approach to vibro acoustic analysis based on the gaussian orthogonal ensemble vibro acoustic analysis of complex systems at higher frequencies faces two challenges how to compute the response without using an excessive number of degrees of freedom dofs and how to quantify the uncertainty of the response due to small spatial variations in geometry material properties and boundary conditions which have a wave scattering effect in this study a general method of analysis is presented that provides an answer to both questions while overcoming most limitations of statistical energy analysis the fundamental idea is to numerically compute an artificial ensemble of realizations for the components of the built up system that are highly sensitive to small random wave scatterers this can be efficiently performed because their eigenvalue spacings and mode shapes conform to gaussian orthogonal ensemble spacings and gaussian random fields respectively the dofs of the overall system are therefore limited to those of the deterministic components and the interface dofs of the random components the method is extensively validated by application to plate structures good agreement between the predicted response probability distributions and the results of detailed parametric probabilistic models is obtained also for cases of low modal overlap single point loading and strong subsystem coupling

similarity solutions of the deformed maxwell bloch system the authors have found similarity reductions for the deformed maxwell bloch system to the fifth and second painleve equations asymptotics of the solutions of these equations which are relevant to two level atomic systems with pumping have also been derived

prolongation structure and linear eigenvalue equations for einstein maxwell fields the einstein maxwell equations for stationary axisymmetric exterior fields are shown to be the integrability conditions of a set of linear eigenvalue equations for pseudopotentials the prolongation structure in the spirit of wahlquist and estabrook 1975 of the einstein maxwell equations contains the su 2 1 lie algebra a new mapping of known solutions to other solutions has been found

an algebraic method for finding a series of exact solutions to integrable and nonintegrable nonlinear evolution equations an algebraic method is devised to uniformly construct a series of exact solutions for general integrable and nonintegrable nonlinear evolution equations compared with most existing tanh methods the jacobi function expansion method or other sophisticated methods the proposed method not only gives new and more general solutions but also provides a guideline to classify the various types of the solutions according to the values of some parameters the solutions obtained in this paper include a polynomial solutions b exponential solutions c rational solutions d triangular periodic wave solutions e hyperbolic and solitary wave solutions and f jacobi and weierstrass doubly periodic wave solutions the efficiency of the method can be demonstrated on a large variety of nonlinear equations such as those considered in this paper new 2 1 dimensional calogero kdv equation 3 1 dimensional jimbo miwa equation symmetric regular long wave equation drinfel d sokolov wilson equation 2 1 dimensional generalized dispersive long wave equation double sine gordon equation calogero degasperis fokas equation and coupled schrodinger boussinesq equation in addition the links among our proposed method the tanh method the extended method and the jacobi function expansion method are also clarified generally

integrable evolution systems based on gerdjikov ivanov equations bi hamiltonian structure finite dimensional integrable systems and n fold darboux transformation a spectral problem and the associated gerdjikov ivanov gi hierarchy of nonlinear evolution equations is presented as a reduction the well known gi equation of derivative nonlinear schrodinger equations is obtained it is shown that the gi hierarchy is integrable in a liouville sense and possesses bi hamiltonian structure moreover the spectral problem can be nonlinearized as a finite dimensional completely integrable system under the bargmann constraint between the potentials and the eigenfunctions in particular an explicit n fold darboux transformation for the gi equation is constructed with the help of a gauge transformation of spectral problems and a reduction technique some explicit solitonlike solutions of the gi equation are given by applying its darboux transformation

darboux polynomial matrices the classical massive thirring model as a study case one way of constructing explicit expressions of solutions of integrable systems of partial differential equations goes via the darboux method this requires the construction of darboux matrices here we introduce a novel algorithm to obtain such matrices in polynomial form our method is illustrated by applying it to the classical massive thirring model and by combining it with the dihedral group of symmetries possessed by this model

backlund transforms of chiral fields the action of the backlund transformations on the axisymmetric chiral fields is investigated in particular it is calculated how the superpotential associated with any chiral field is affected by the backlund transformations

an algebraic method to construct the darboux matrix we present an effective procedure to construct the 1 soliton darboux matrix our approach based on the zakharov shabat mikhailov s dressing method is especially useful in the case of non canonical normalization and for non isospectral linear problems the construction is divided into two steps first we represent a given linear problem as a system of some algebraic constraints on two matrices in this context we introduce and discuss invariants of the darboux matrix second we derive the darboux matrix demanding that it preserves the algebraic constraints in particular we consider in details the restrictions imposed by various reduction groups on the form of the darboux matrix

algebraic construction of the darboux matrix revisited we present algebraic construction of darboux matrices for 1 1 dimensional integrable systems of nonlinear partial differential equations with a special stress on the nonisospectral case we discuss different approaches to the darboux backlund transformation based on different dependences of the darboux matrix polynomial sum of partial fractions or the transfer matrix form we derive symmetric n soliton formulae in the general case the matrix spectral parameter and dressing actions in loop groups are also discussed we describe reductions to twisted loop groups unitary reductions the matrix lax pair for the kdv equation and reductions of chiral models harmonic maps to su n and to grassmann spaces we show that in the kdv case the nilpotent darboux matrix generates the binary darboux transformation the paper is intended as a review of known results usually presented in a novel context but some new results are included as well e g general compact formulae for n soliton surfaces and linear and bilinear constraints on the nonisospectral lax pair matrices which are preserved by darboux transformations

nonautonomous integrable nonlinear schrodinger equations with generalized external potentials inhomogeneous nonlinear schrodinger equations are constructed systematically using the covariance with respect to the darboux transformation the darboux invariants and the spectral parameter are functions of time and space which result in equations describing nonautonomous solitons moving in generalized external potentials all the known inhomogeneous nonlinear schrodinger equations as well as new ones of a more generalized form can be derived from the constructed equation one and two soliton solutions are explicitly constructed using the darboux transformation

parallel machine scheduling with deteriorating jobs and rejection we consider several parallel machine scheduling problems in which the processing time of a job is a simple linear increasing function of its starting time and jobs can be rejected by paying penalties the objective is to minimize the scheduling cost of the accepted jobs plus the total penalty of the rejected jobs three variations of the scheduling cost are considered in this paper the first is the makespan the second is the total weighted completion time for simple linear deterioration and the third is the total completion time for the former two problems we propose two fully polynomial time approximation schemes to solve them when the number of machines is fixed for the last problem we present an optimal o n 2 time dynamic programming algorithm when the deteriorating rates are equal for all jobs

response variance prediction in the statistical energy analysis of built up systems in the statistical energy analysis sea of high frequency noise and vibration a complex engineering structure is represented as an assembly of subsystems the response of the system to external excitation is expressed in terms of the vibrational energy of each subsystem and these energies are found by employing the principle of power balance strictly the computed energy is an average taken over an ensemble of random structures and for many years there has been interest in extending the sea prediction to the variance of the energy a variance prediction method for a general built up structure is presented here closed form expressions for the variance are obtained in terms of the standard sea parameters and an additional set of parameters alpha k that describe the nature of the power input to each subsystem k and alpha ks that describe the nature of the coupling between subsystems k and s the theory is validated by comparison with monte carlo simulations of plate networks and structural acoustic systems

constructing of new exact solutions to the gkdv mkdv equation with any order nonlinear terms by g g expansion method abstract the g g expansion method is introduced to construct more general exact travelling wave solutions to the generalized kdv mkdv equation with any order nonlinear terms as a result hyperbolic function solution trigonometric function solution and rational solution with parameters are obtained when the parameters take up special values the solitary waves are also derived from the travelling wave solutions the g g expansion method presents a wider applicability for handling nonlinear wave equations

a discrete generalized coupled dispersionless integrable system and its multisoliton solutions abstract an integrable discretization of generalized coupled dispersionless dgcd integrable system via lax pair is presented a lax pair for the dgcd system is defined a darboux transformation is used on the lax pair to obtain multi soliton solutions of the dgcd system the solutions are expressed in terms of quasideterminants explicit expressions of discrete one and two soliton solutions are obtained for the s u 2 case by using properties of quasideterminants we also study continuous analogue of the dgcd system by applying continuum limit

a hierarchy of coupled korteweg de vries equations and the normalisation conditions of the hilbert riemann problem the authors discuss the normalisation conditions of the hilbert riemann problem which is of importance for the construction of the ladder of soliton solutions for a given spectral problem they provide the prescription for constructing the appropriate normalisation condition all this is applied to a new hierarchy of coupled korteweg de vries equations to find the soliton solution which displays some peculiar phenomena

the level crossing rates and associated statistical properties of a random frequency response function abstract this work is concerned with the statistical properties of the frequency response function of the energy of a random system earlier studies have considered the statistical distribution of the function at a single frequency or alternatively the statistics of a band average of the function in contrast the present analysis considers the statistical fluctuations over a frequency band and results are obtained for the mean rate at which the function crosses a specified level or equivalently the average number of times the level is crossed within the band results are also obtained for the probability of crossing a specified level at least once the mean rate of occurrence of peaks and the mean trough to peak height the analysis is based on the assumption that the natural frequencies and mode shapes of the system have statistical properties that are governed by the gaussian orthogonal ensemble goe and the validity of this assumption is demonstrated by comparison with numerical simulations for a random plate the work has application to the assessment of the performance of dynamic systems that are sensitive to random imperfections

statistical energy analysis with fuzzy parameters to handle populations of structures statistical modal energy distribution analysis smeda approach was developed to enlarge the application field of statistical energy analysis sea when equipartition of modal energies is not achieved smeda gives more precise results than standard sea when compared to exact energy response of a deterministic system in the case of low modal overlap heterogeneous systems or point excitation the present paper was initiated by this question when considering a population of similar structures each of them being described by smeda do the ensemble averaged energies of subsystem and injected power tend to satisfy sea equations in other terms despite the non equipartition of energy observed on each element of the population of structures does the ensemble averaging leads to sea equation where equipartition of energy is assumed the response to that question that rises from this paper is yes if the terms of the sea equation are fuzzy numbers it results that the energy response given by the model can be interpreted using fuzzy numbers theory

the sine gordon equation on time scales abstract we formulate and discuss integrable analogue of the sine gordon equation on arbitrary time scales this unification contains the sine gordon equation discrete sine gordon equation and the hirota equation doubly discrete sine gordon equation as special cases we present the lax pair check compatibility conditions and construct the darboux backlund transformation finally we obtain a soliton solution on arbitrary time scale the solution is expressed by the so called cayley exponential function

an effective method to compute n fold darboux matrix and n soliton surfaces fairly simple formulas for an n fold darboux matrix and an n soliton addition to an arbitrary soliton surface embedded in e3 are proven they depend directly on the background wave function and are evidently symmetric with respect to n added solitons as an example an explicit expression for the interaction of n solitons on a single vortex filament is presented moreover there is given a simplified version of the n soliton formulas of neugebauer and meinel

the structure of spectral problems and geometry hyperbolic surfaces in e3 working in the framework of sym s soliton surfaces approach we point out that some simple assumptions about the structure of linear spectral problems of the theory of solitons lead uniquely to the geometry of some special immersions in this paper we consider general su 2 spectral problems under some very weak assumptions they turn out to be associated with hyperbolic surfaces surfaces of negative gaussian curvature immersed in three dimensional euclidean space and especially with the so called bianchi surfaces

bicomplexes and backlund transformations a bicomplex is a simple mathematical structure in particular associated with completely integrable models the conditions defining a bicomplex are a special form of a parameter dependent zero curvature condition we generalize the concept of a darboux matrix to bicomplexes and use it to derive backlund transformations for several models the method also works for moyal deformed equations with a corresponding deformed bicomplex

on a 2 1 dimensional integrable ernst type equation a strong 2 1 dimensional integrable extension of ernst s equation of general relativity is proposed its richness is demonstrated by means of various canonical dimensional reductions and specializations which lead to formal analogues of well known 1 1 and 2 1 dimensional integrable systems such as the self induced transparency equations the konopelchenko rogers equations a 2 1 dimensional darboux system descriptive of conjugate coordinate systems a single 2 1 dimensional sine gordon equation and the equations representing its backlund transformation a darboux levi type transformation is given and its compatibility with the above mentioned reductions is shown

the darboux backlund transformation for the static 2 dimensional continuum heisenberg chain we construct the darboux backlund transformation for the sigma model describing static configurations of the 2 dimensional classical continuum heisenberg chain the transformation is characterized by a non trivial normalization matrix depending on the background solution in order to obtain the transformation we use a new more general spectral problem

multi soliton propagation in a generalized inhomogeneous nonlinear schrodinger maxwell bloch system with loss gain driven by an external potential in this paper we introduce a system of the nonlinear schrodinger maxwell bloch equation with variable coefficients which represents the propagation of optical pulses in an inhomogeneous erbium doped fiber with loss gain driven by an external potential the one and two soliton solutions in explicit forms are generated by using the darboux transformation and the associated lax pair we consider the distributed amplification system and some main features of the solutions are demonstrated graphically we also consider the concept of soliton propagation in a dispersion managed erbium doped fiber and through symbolic computation we have carried out our study from an analytic viewpoint

response variance prediction for uncertain vibro acoustic systems using a hybrid deterministic statistical method imperfections during the manufacturing process can cause significant variations in the noise and vibration levels exhibited by nominally identical structures any response calculations employed during the design process should ideally take account of these uncertainties and predict the expected range in performance recently a hybrid method has been developed to predict the ensemble average response of a built up system by combining a deterministic model of parts of the system with a statistical model of other components shorter p j and langley r s 2005 j sound vib 288 669 700 in this paper the method is extended to predict the ensemble variance of the response expressions are derived for the variance of the vibrational energies in the statistical components and for the variance of the cross spectrum of the response of the deterministic components which augment the mean values of these quantities predicted by the original theory the method employs a nonparametric model of uncertainty in the sense that the statistical components are taken to carry diffuse wave fields and this obviates the requirement for a detailed description of the system uncertainties the method is validated by application to a range of coupled plate structures and good agreement with detailed monte carlo simulations is found

scheduling linear deteriorating jobs with rejection on a single machine we consider several single machine scheduling problems in which the processing time of a job is a linear function of its starting time and jobs can be rejected by paying penalties the objectives are to minimize the makespan the total weighted completion time and the maximum lateness tardiness plus the total penalty of the rejected jobs we show that these problems are np hard and design algorithms based on dynamic programming including pseudo polynomial time optimal algorithms and fully polynomial time approximation schemes to solve them

darboux transformation of the generalized coupled dispersionless integrable system the darboux transformation on matrix solutions to the generalized coupled dispersionless integrable system based on a non abelian lie group is studied and the solutions are shown to be expressed in terms of quasideterminants as an explicit example the darboux transformation on scalar solutions to the system based on the lie group su 2 is discussed in detail and the solutions are shown to be expressed as ratios of determinants

a family of completely integrable multi hamiltonian systems explicitly related to some celebrated equations by introducing a spectral problem with an arbitrary parameter we derive a kaup newell type hierarchy of nonlinear evolution equations which is explicitly related to many important equations such as the kundu equation the kaup newell kn equation the chen lee liu cll equation the gerdjikov ivanov gi equation the burgers equation the modified korteweg devries mkdv equation and the sharma tasso olver equation it is shown that the hierarchy is integrable in liouville s sense and possesses multi hamiltonian structure under the bargann constraint between the potentials and the eigenfunctions the spectral problem is nonlinearized as a finite dimensional completely integrable hamiltonian system the involutive representation of the solutions for the kaup newell type hierarchy is also presented in addition an n fold darboux transformation of the kundu equation is constructed with the help of its lax pairs and a reduction technique according to the darboux transformation the solutions of the ku

darboux transformations and exact solutions of two dimensional a2n 2 toda equation the darboux transformations for two dimensional a2n 2 toda equation are constructed the lowest degree of the darboux transformation is 2 2n 1 if all the spectral parameters are complex or 2n 1 if one spectral parameter is real exact solutions are written down by computing the darboux transformations explicitly

the effect of generalised force correlations on the response statistics of a harmonically driven random system if the physical properties of a structural component are sufficiently random then the statistical distribution of the natural frequencies and mode shapes tends to a universal distribution associated with the gaussian orthogonal ensemble goe of random matrices previous work has exploited this result to yield expressions for the relative variance of the energy of the response of a random system to harmonic excitation the derivation of these expressions employed random point process theory and in the theoretical development it was assumed that the modal generalised forces were uncorrelated although this assumption is often valid there are cases in which correlations between the generalised forces can significantly affect the response variance and in the present work the existing theory is extended to include correlations of this type the extended theory is applicable to both single frequency responses and to band average responses and the developed closed form expressions are validated by comparison with direct simulations for a random plate structure

neugebauer kramer solutions of the ernst equation in hirota s direct method we prove analytically the sasa satsuma conjecture which states that their solution of bilinear form of the ernst equation gives the neugebauere kramer solution in particular cases this proof relates hirota s direct method with the backlund transformation method and opens the way towards the comprehensive interpretation of the ernst equation

quasideterminant solutions of an integrable chiral model in two dimensions the darboux transformation is used to obtain multisoliton solutions of the chiral model in two dimensions the matrix solutions of the principal chiral model and its lax pair are expressed in terms of quasideterminants the iteration of the darboux transformation gives the quasideterminant multisoliton solutions of the model it has been shown that the quasideterminant multisoliton solution of the chiral model is the same as obtained by zakharov and mikhailov using the dressing method based on the matrix riemann hilbert problem

geometrical and gauge equivalence of the generalized hirota heisenberg and wkis equations with linear inhomogeneities integrable evolution equations can take several equivalent forms in a geometrical sense here we consider the equivalence of generalized versions involving linear inhomogeneities of three important nonlinear evolution equations namely the hirota heisenberg ferromagnetic spin and wadati konno ichikawa shimizu wkis equation through a moving helical space curve formalism and stereographic representation from the geometrical consideration we also construct suitable 2 2 matrix linear eigenvalue equations involving however non isospectral flow the eigenvalues evolve in time however these systems are also gauge equivalent we briefly analyse the scattering problem and show that infinite number of constants of motion can exist for these systems