the painleve property for partial differential equations in this paper we define the painleve property for partial differential equations and show how it determines in a remarkably simple manner the integrability the backlund transforms the linearizing transforms and the lax pairs of three well known partial differential equations burgers equation kdv equation and the modified kdv equation this indicates that the painleve property may provide a unified description of integrable behavior in dynamical systems ordinary and partial differential equations while at the same time providing an efficient method for determining the integrability of particular systems

sufficiency and duality in nonsmooth multiobjective optimization involving generalized f α π d type i functions in this paper new classes of generalized f a p d type i functions are introduced for a nonsmooth multiobjective programming problem based upon these generalized functions sufficient optimality conditions are established weak strong and strict converse duality theorems are also derived for wolfe and mond weir type multiobjective dual programs in order to relate the efficient and weak efficient solutions of primal and dual problems

mean value in invexity analysis abstract in this paper a generalization of the mean value theorem is considered in the case of functions defined on an invex set with respect to which is not necessarily connected

characterization of a condition related to a class of preinvex functions in the theory of invex functions a very important role is played by the so called condition c we present a convenient characterization of this condition in terms of starlike sets and projections

a variational like inequality for multifunctions with applications abstract we study a variational like inequality problem for a multifunction a certain relevant complementarity problem is defined we establish some existence theorems for the above two problems an application to convex mathematical programming is also shown

invex sets and preinvex functions on riemannian manifolds the concept of a geodesic invex subset of a riemannian manifold is introduced geodesic invex and preinvex functions on a geodesic invex set with respect to particular maps are defined the relation between geodesic invexity and preinvexity of functions on manifolds is studied using proximal subdifferential certain results concerning extremum points of a non smooth geodesic preinvex function on a geodesic invex set are obtained the main value inequality and the mean value theorem in invexity analysis are extended to cartan hadamard manifolds

a proof for antczak s mean value theorem in invexity analysis abstract this paper provides another proof for antczak s mean value theorem in invexity analysis

generalized riccati equation expansion method and its application to the 3 1 dimensional jumbo miwa equation based on the computerized symbolic system maple and a riccati equation a generalized riccati equation expansion method for constructing soliton like solutions of non linear evolution equations nees is presented by a new general ansatz the proposed method is more powerful than most of the existing tanh methods the extended tanh function method the modified extended tanh function method and generalized hyperbolic function method by use of the method we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some nees making use of the method we study the the 3 1 dimensional jumbo miwa equation and obtain rich new families of the exact solutions including the non travelling wave and coefficient functions soliton like solutions singular soliton like solutions periodic form solutions

generalized mixed quasi variational like inequalities in this paper we use the auxiliary principle technique to suggest and analyze some iterative methods for solving generalized mixed quasi variational like inequalities we show that the convergence of the proposed method requires either pseudomonotonicity or partially relaxed strongly monotonicity under some mild condition as special cases one can obtain a number of new and known algorithms for solving variational inequalities and complementarity problems our results represent significant and important refinements of the previously known results

efficiency through variational like inequalities with lipschitz functions in this work first we introduce several notions of invexity and pseudoinvexity for a locally lipschitz function by means of the generalized jacobian we study relationships between these concepts in particular the implications between preinvexity and invexity next we obtain necessary and sufficient optimality conditions for efficient and weak efficient solutions of finite dimensional non necessarily pareto vector optimization problems with locally lipschitz objective functions through solutions of vector variational like inequality problems these conditions are stated via the generalized jacobian and under pseudoinvexity hypotheses and they show that a vector optimization problem can be reformulated as a vector variational like inequality problem this work extends and improves several previous papers where the objective function of the vector optimization problem is assumed to be differentiable or being locally lipschitz the authors consider the componentwise subdifferential based on the clarke s generalized gradients of the components of the objective function throughout the paper some simple examples are given in order to illustrate the main concepts and results

using waveform relaxation methods to approximate neutral stochastic functional differential equation systems this paper extends the waveform relaxation wr method to neutral stochastic functional differential equations the linear convergence theory of the continuous time wr method is established in the mean square sense when the coefficients of stochastic differential equation systems satisfy the lipschitz condition and the contractive mapping the discrete time wr method based on the euler scheme which is used in an actual implementation was also studied it turns out that the sequence produced by this method converges linearly to the euler approximate solution which is convergent in addition we prove that the preceding methods are convergent superlinearly if the neutral term does not been split finally the theory is applied to a one dimensional model problem and checked against results obtained by numerical experiments

solitonic excitations and interactions in an α helical protein modeled by three coupled nonlinear schrodinger equations with variable coefficients governing the molecular excitations associated with bioenergy transport in an helical protein through the soliton modes three coupled higher order nonlinear schrodinger equations with variable coefficients are investigated via symbolic computation using bell polynomials a bilinear form and backlund transformation are derived for this model furthermore explicit n soliton solutions are constructed in terms of the double wronskian determinant solitonic excitations are found to remain stable against the disorders of the parameters under certain constraints finally propagation characteristics and interactions of the solitonic excitations are discussed soliton amplitudes are related to the energy modulation coefficients and both the soliton properties and energy distribution during the interactions are affected by the inhomogeneity coefficients of the protein with time dependent disorders

delay dependent estimates for waveform relaxation methods for neutral differential functional systems in this paper the problem of delay dependent error estimates for waveform relaxation methods applied to volterra type systems of functional differential equations of neutral type including systems of differential algebraic equations is discussed under a lipschitz condition with delay dependent right hand side imposed on the so called splitting function it is shown how the error estimates depend on the character of delays and that for this reason they are better than the known error estimates for relaxation methods it is proved that under some assumptions the exact solution can be obtained after a finite number of steps of the iterative process i e we prove that the waveform relaxation methods have the same property as the classical method of steps for solving delay differential equations with nonvanishing delays we also show the convergence of the waveform relaxation method without assuming that the spectral radius of the corresponding matrix related to the lipschitz coefficients for the neutral argument is less than one

backlund transformation and multi soliton solutions for a 2 1 dimensional korteweg de vries system via symbolic computation abstract in this paper the 2 1 dimensional korteweg de vries system is symbolically investigated by the bilinear method the n soliton solution is presented then based on the backlund transformation in bilinear form a new backlund transformation is obtained and new representation of the n soliton solution is derived a class of novel multi soliton solutions are obtained by the new backlund transformation and the availability of symbolic computation is demonstrated

waveform relaxation methods for functional differential systems of neutral type abstract we investigate continuous time and discretized waveform relaxation iterations for functional differential systems of neutral type it is demonstrated that continuous time iterations converge linearly for neutral equations and superlinearly when the right hand side is independent of the history of the derivative of the solution the error bounds for discretized iterations are also obtained and some implementation aspects are discussed numerical results are presented which indicate a potential speedup of this technique as compared with the classical approach based on discrete variable methods

bell polynomial manipulations on the backlund transformations and lax pairs for some soliton equations with one tau function in the framework of bell polynomial manipulations under investigation hereby are three single field bilinearizable equations the 1 1 dimensional shallow water wave model boiti leon manna pempinelli model and 2 1 dimensional sawada kotera model based on the concept of scale invariance a direct and unifying bell polynomial scheme is employed to achieve the backlund transformations and lax pairs associated with those three soliton equations note that the bell polynomial expressions and bell polynomial typed backlund transformations for those three soliton equations can be respectively cast into the bilinear equations and bilinear backlund transformations with symbolic computation consequently it is also shown that the bell polynomial typed backlund transformations can be linearized into the corresponding lax pairs

hemiequilibrium like problems abstract in this paper we introduce and consider a new class of equilibrium problems known as hemiequilibrium like problems this new class includes hemiequilibrium equilibrium like problems and several classes of variational inequalities as special cases a number of iterative methods for solving hemiequilibrium like problems are suggested and analyzed by using the auxiliary principle technique we also study the convergence analysis of these iterative methods under some mild conditions the results obtained in this paper can be considered as a novel application of the auxiliary principle technique

waveform relaxation for functional differential equations the convergence of waveform relaxation techniques for solving functional differential equations is studied new error estimates are derived that hold under linear and nonlinear conditions for the right hand side of the equation sharp error bounds are obtained under generalized time dependent lipschitz conditions the convergence of the waveform method and the quality of the a priori error bounds are illustrated by means of extensive numerical data obtained by applying the method of lines to three partial functional differential equations

convergence of waveform relaxation methods for differential algebraic systems this paper gives sufficient conditions for existence and uniqueness of solutions and for the convergence of picard iterations and more general waveform relaxation methods for differential algebraic systems of neutral type the results are obtained by the contraction mapping principle on banach spaces with weighted norms and by the use of the perron frobenius theory of nonnegative and nonreducible matrices it is demonstrated that waveform relaxation methods are convergent faster than the classical picard iterations

relationships between pre invex concepts abstract it is well known that some properties of convex optimization problems especially sufficient conditions for optimality and duality conditions are preserved when convexity is weakened to pre invexity however there are several distinct pre invex concepts b vex b pre invex pre univex p r pre invex and these are not equivalent the pre invexity concepts mentioned above have also some properties which are characteristic and invariant for functions belonging to these classes of functions

averaged dynamics of optical pulses described by a nonlinear schrodinger equation with periodic coefficients a nonlinear schrodinger equation with periodic coefficients as it appears e g in nonlinear optics is considered the high frequency variable part of the dispersion may be even much larger than the mean value the ratio of the length of the dispersion map to the period of a solution is assumed as one small parameter the second one corresponds to the integral over the variable part of the dispersion for the averaged dynamics we propose a procedure based on the bogolyubov method as a result we obtain the asymptotic equation in the dominating order as well as with the next corrections the equation is valid for all combinations of the small parameters the explicit forms of the coefficients are presented for a two step dispersion map with an exponential loss function the forms of the bright and black soliton solutions are discussed the results are compared to those from other averaging methods namely the multiple scale method and the method based on lie transformations

on the convergence of waveform relaxation methods for differential functional systems of equations in this paper the convergence of a waveform relaxation method applied to an initial value problem for the volterra functional differential system is discussed it is shown that the method is convergent under the assumption that the splitting function satisfies only the one side lipschitz condition with respect to some arguments and the lipschitz condition with respect to the others the conditions given in the paper also guarantee the existence and uniqueness of the solution to the initial problem discussed in the paper the convergence of the perturbed continuous time waveform relaxation method is also discussed

types of solutions of the variable coefficient nonlinear schrodinger equation with symbolic computation by using hirota s bilinear method and symbolic computation solutions for a variable coefficient nonlinear schrodinger equation are obtained theoretically it is found that the type of the solutions changes with the different choices of the group velocity dispersion coefficient beta 2 z according to those solutions the relevant properties and features of physical and optical interest are illustrated in addition an effective technique for controlling the shape of the pulses is presented the results of this paper will be valuable to the study of the future development of ultrahigh rate and long distance optical communication systems

contractivity of waveform relaxation runge kutta iterations and related limit methods for dissipative systems in the maximum norm contractivity properties of runge kutta methods are analyzed with suitable interpolation implemented using waveform relaxation strategy for systems of ordinary differential equations that are dissipative in the maximum norm in general this type of implementation which is quite appropriate in a parallel computing environment improves the stability properties of runge kutta methods as a result of this analysis a new class of methods is determined which is different from runge kutta methods but closely related to them and which combines its high order of accuracy and unconditional contractivity in the maximum norm this is not possible for classical runge kutta methods

linear acceleration of picard lindelof iteration the possibility to accelerate the picard lindelof process by taking linear combinations of the iterates is discussed the convergence is studied on infinitely long intervals

a note on invex problems with nonnegative variable we provide sufficient optimality conditions involving invexity for mathematical programming problems with nonnegative variable we also show that upon certain assumptions on the scaling function these problems are convex transformable hence certain associated convex problems should be solved some applications are shown

estimating waveform relaxation convergence critical limitations of the waveform relaxation method concern the unsolved problems of estimating convergence and controlling the iteration in this paper waveform relaxation is applied to a linear second order model system and is studied in the laplace domain by placing the iteration in a weighted space computable estimates for a window of rapid convergence are developed numerical experiments illustrate the utility of the approach

parallel treatment of a class of differential algebraic systems in this paper we derive an asynchronous method for the parallel solution of a class of index one differential algebraic systems with initial values these systems are in the form left begin array l f x prime t x t y t t 0 g x t y t t 0 3pt x t 0 x 0 end array right g x y t 0 must be solvable with respect to y this study allows us to give asynchronous extensions of the waveform relaxation method

bell polynomial approach and n soliton solution for the extended lotka volterra equation in plasmas symbolically investigated in this paper is the extended lotka volterra elv equation which can govern the kinetics of the discrete peaks of the weak langmuir turbulence in plasmas without the linear damping and random noise binary bell polynomials are applied to the bilinearization of the discrete system bilinear backlund transformation of the elv equation is constructed n soliton solution in terms of the extended casorati determinant is also presented and verified propagation and interaction behaviors of the langmuir turbulence are analyzed it is demonstrated that the number of the interacting langmuir waves can influence the soliton velocity and amplitude as well as the collision phase shift graphic illustrations of the solitonic collisions show that the repulsion effects and nonlinear interactions are also associated with the number of the interacting langmuir waves

exact travelling wave solutions for a generalized nonlinear schrodinger equation a wide class of exact travelling wave solutions of a generalized nonlinear schrodinger equation gnls is obtained and analysed in detail this class of solutions incorporates bright and dark solitary waves periodic waves unbounded waves and other solitary waves as asymptotic limits of the periodic or unbounded modes the method of analysis adopted is based on reducing the gnls to an ordinary differential equation and studying the phase plane of the resulting dynamical system application of the obtained results to the problem of propagation of femtosecond duration pulses in nonlinear optical fibres is also discussed

symbolic computation and new families of exact soliton like solutions to the integrable broer kaup bk equations in 2 1 dimensional spaces in this paper new families of soliton like solutions are obtained for 2 1 dimensional integrable broer kaup equations by using the symbolic computation method developed by gao and tian sample solutions obtained from these methods are presented solitary wave solutions are merely a special case in one family the method can also be extended to other types of nonlinear evolution equations in mathematical physics

g pre invex functions in mathematical programming in the present paper we introduce the concept of g pre invex functions with respect to h defined on an invex set with respect to h these function unify the concepts of nondifferentiable convexity pre invexity and r pre invexity furthermore relationships of g pre invex functions to various introduced earlier pre invexity concepts are also discussed some geometric properties of this class of functions are also derived finally optimality results are established for optimization problems under appropriate g pre invexity conditions

on the convergence of iterative methods for general differential algebraic systems in this paper the existence and uniqueness of solutions to quite general classes of integro algebraic systems and differential algebraic systems are investigated the convergence of different iterative processes of solving such systems including waveform relaxation methods is also investigated there are given constructive sufficient conditions under which the solutions exist and are unique and the considered iterative processes are convergent

symbolic computation backlund transformation and analytic n soliton like solution for a nonlinear schrodinger equation with nonuniformity term from certain space laboratory plasmas abstract with symbolic computation a bilinear backlund transformation is presented for a nonlinear schrodinger equation with nonuniformity term from certain space laboratory plasmas and correspondingly the one soliton like solution is derived from the backlund transformation simultaneously the n soliton like solution in double wronskian form is also given besides the authors verify that the n 1 and n soliton like solutions satisfy the backlund transformation the results obtained in this paper might be valuable for the study of the nonuniform media

existence and iterative approximations of solutions for mixed quasi variational like inequalities in banach spaces abstract in this paper we introduce and investigate a new class of mixed quasi variational like inequalities in reflexive banach spaces by applying a minimax inequality due to ding tan and a lemma due to chang we establish some existence and uniqueness results of solution for the mixed quasi variational like inequality next by using a kkm theorem due to fan and an auxiliary principle technique due to cohen we suggest two iterative algorithms and study the convergence criteria of iterative sequences generated by the iterative algorithms our results extend improve and unify several known results in the literature

dynamic iteration methods applied to linear dae systems abstract we continue the study of the convergence of dynamic iteration methods by applying them to linear dae systems we show that convergence rate can be studied by similar means as for ode s and that it is critical for convergence to preserve the structure of the dae system when it is split for the iteration

on error estimates for waveform relaxation methods for delay differential equations in this paper the problem of delay dependent error estimates for waveform relaxation methods applied to systems of delay differential equations is discussed under suitable conditions imposed on the so called splitting function it is shown how the error estimates depend on the character of delays and how much these estimates are better than the known error estimates for relaxation methods we attempt to derive the error estimates as sharp as possible under the assumed conditions our approach takes into account the specific properties of the considered equations it is also proved that under some assumptions the exact solution can be obtained after a finite number of steps of the iterative process i e we prove that the waveform relaxation methods have the same property as the classical method of steps for solving delay differential equations with nonvanishing delays from the given estimates the number of these steps can be found

sufficiency and duality in nondifferentiable multiobjective programming involving generalized type i functions abstract recently hachimi and aghezzaf defined generalized f d type i functions a new class of functions that unifies several concepts of generalized type i functions in this paper the generalized f d type i functions are extended to nondifferentiable functions by utilizing the new concepts we obtain several sufficient optimality conditions and prove mixed type and mond weir type duality results for the nondifferentiable multiobjective programming problem

a mean value theorem in asplund spaces abstract in this paper a nonsmooth mean value theorem in asplund spaces under invexity is provided

computing periodic solutions of linear differential algebraic equations by waveform relaxation we propose an algorithm which is based on the waveform relaxation wr approach to compute the periodic solutions of a linear system described by differential algebraic equations for this kind of two point boundary problems we derive an analytic expression of the spectral set for the periodic wr operator we show that the periodic wr algorithm is convergent if the supremum value of the spectral radii for a series of matrices derived from the system is less than 1 numerical examples where discrete waveforms are computed with a backward difference formula further illustrate the correctness of the theoretical work in this paper

nonsmooth invex functions and sufficient optimality conditions in this paper the various definitions of nonsmooth invex functions are gathered in a general scheme by means of the concept of k directional derivative characterizations of nonsmooth k invexity are derived as well as results concerning constrained optimization without any assumption of convexity of the k directional derivatives

multigrid waveform relaxation on spatial finite element meshes the continuous time case the waveform relaxation method and its multigrid acceleration are studied as solution procedures for the system of ordinary differential equations obtained by finite element discretisation of a linear parabolic initial boundary value problem the convergence properties of the continuous time algorithm are theoretically investigated on finite length and infinite length time intervals in addition quantitative convergence estimates and numerical results are presented for one dimensional and two dimensional model problems

convergence analysis of waveform relaxation methods for neutral differential functional systems in this paper the problems of convergence and superlinear convergence of continuous time waveform relaxation method applied to volterra type systems of neutral functional differential equations are discussed under a lipschitz condition with time and delay dependent right hand side imposed on the so called splitting function more suitable conditions about convergence and superlinear convergence of continuous time wr method are obtained we also investigate the initial interval acceleration strategy for the practical implementation of the continuous time waveform relaxation method i e discrete time waveform relaxation method it is shown by numerical results that this strategy is efficacious and has the essential acceleration effect for the whole computation process

on sufficiency of the kuhn tucker conditions if all the functions fo x f x f x are convex on c then these conditions are also sufficient various classes of functions have been defined for the purpose of weakening this limitation of convexity in mathematical programming mangasarian 11 has speculated that pseudo convexity of x and quasiconvexity off x are the weakest conditions that can be imposed so that the above conditions are sufficient for optimality it will be shown that there are other wide classes of functions for which the conditions are sufficient 545

soliton solutions backlund transformation and wronskian solutions for the extended 2 1 dimensional konopelchenko dubrovsky equations in fluid mechanics abstract this paper is to investigate the extended 2 1 dimensional konopelchenko dubrovsky equations which can be applied to describing some phenomena in the stratified shear flow the internal and shallow water waves and plasmas bilinear form equations are transformed from the original equations and n soliton solutions are derived via symbolic computation bilinear form backlund transformation and single soliton solution are obtained and illustrated wronskian solutions are constructed from the backlund transformation and single soliton solution

nondifferentiable multiobjective programming under generalized di invexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce new concepts of d i invexity and generalized d i invexity in which each component of the objective and constraint functions is directionally differentiable in its own direction d i new fritz john type necessary and karush kuhn tucker type necessary and sufficient optimality conditions are obtained for a feasible point to be weakly efficient efficient or properly efficient moreover we prove weak strong converse and strict duality results for a mond weir type dual under various types of generalized d i invexity assumptions

solitonic solutions for a variable coefficient variant boussinesq system in the long gravity waves variable coefficient variant boussinesq vcvb system is able to describe the nonlinear and dispersive long gravity waves traveling in two horizontal directions with varying depth in this paper with symbolic computation a lax pair associated with the vcvb system under some constraints for variable coefficients is derived and based on the lax pair two sorts of basic darboux transformations are presented by applying the darboux transformations some solitonic solutions are obtained with the relevant constraints given in the text in addition the vcvb system is transformed to a variable coefficient broer kaup system solitonic solutions and procedure of getting them could be helpful to solve the nonlinear and dispersive problems in fluid dynamics

the use of backlund transformations in obtaining n soliton solutions in wronskian form the wronskian formulation of the n soliton solutions of various nonlinear evolution equations modified korteweg de vries with both zero and non zero asymptotic conditions sine gordon korteweg de vries kadomtsev petviashvili and boussinesq equations are obtained by inductive use of backlund transformations in hirota s 1980 bilinear notation

optimality and duality for generalized fractional programming involving nonsmooth f ρ convex functions using a parametric approach we establish necessary and sufficient conditions and derive duality theorems for a class of nonsmooth generalized minimax fractional programming problems containing f r convex functions

some quantum integral inequalities via preinvex functions in this paper we obtain some new quantum analogues of hermite hadamard and iyengar type inequalities for some classes of preinvex functions some special cases are also discussed

nondifferentiable multiobjective programming under generalized d univexity abstract in this paper we are concerned with a nondifferentiable multiobjective programming problem with inequality constraints we introduce four new classes of generalized convex functions by combining the concepts of weak strictly pseudoinvex strong pseudoinvex weak quasi invex weak pseudoinvex and strong quasi invex functions in aghezzaf and hachimi numer funct anal optim 22 2001 775 d invex functions in antczak europ j oper res 137 2002 28 and univex functions in bector et al univex functions and univex nonlinear programming proc admin sci assoc canada 1992 p 115 by utilizing the new concepts we derive a karush kuhn tucker sufficient optimality condition and establish mond weir type and general mond weir type duality results for the nondifferentiable multiobjective programming problem

nonlinear pulse propagation in dispersion managed system abstract we study nonlinear pulse propagation in an optical transmission system with dispersion managements this is particularly important for designing an ultra fast and long haul communication system in the next generation there exists a quasi stationary pulse solution in such a system whose width and chirp are rapidly oscillating with the period of dispersion management this pulse also has several new features such as enhanced power when compared with the soliton case with a uniform dispersion and reduction of timing jitter in a wavelength division multiplexed system the method used here is so called the guiding center or normal form theory based on the lie transform and the averaging method for the case of a small dispersion management the core equation obtained as the normal form is given by the nonlinear schrodinger nls equation with a small correction while for the case with a rather large management the core equation is shown to be the nls equation having a nontrapping quadratic potential because of this potential a steady pulse propagating in such a system requires enhanced power

numerical solutions of a variable coefficient nonlinear schrodinger equation for an inhomogeneous optical fiber abstract this paper investigates a variable coefficient nonlinear schrodinger equation for an inhomogeneous optical fiber numerical one and two solitonic envelopes of the electrical field via the fourth order split step runge kutta split step fourier and runge kutta methods with equal grids in the axis and equal grids in the axis are graphically presented respectively where and represent the retarded time and normalized distance along the fiber 2 norm of the relative errors between the analytical solutions under the painleve integrability condition and numerical solutions are given where the cpu time is also shown relative errors and cpu time of the numerical one and two soliton solutions with equal grids in the axis are bigger than those with equal grids in the axis which does not mean that the results with equal grids in the axis are infeasible compared with the numerical solutions with equal grids in the axis those with equal grids in the axis are closer to the analytical solutions without the painleve integrability condition with respect to the relative errors and cpu time one could choose the split step fourier method to derive the numerical one soliton solutions while the numerical two soliton solutions are gotten with the rk method the attenuation coefficient makes the amplitudes of the solitons decrease the group velocity dispersion coefficient leads to the periodic solitons while the effect of the attenuation coefficient is more obvious than that of the nonlinearity parameter effects of r 1 and i 1 on the solitonic weak interaction between the two solitons are investigated solitonic weak interaction between the two solitons enhances with r 1 and i 1 increasing where r 1 and i 1 are the frequencies of the two solitons

n fold darboux transformation and solitonic interactions of a variable coefficient generalized boussinesq system in shallow water abstract under consideration in this paper is a variable coefficient generalized boussinesq system for the long weakly nonlinear and weakly dispersive surface waves in shallow water with the aid of symbolic computation n fold darboux transformation n dt is constructed for that system analytic solutions of the system are obtained via the n dt elastic interactions of three bell shaped and periodic bell shaped solitons are obtained fusion interactions and periodic fusion fission interactions of the solitary waves are graphically analyzed which are inelastic

multi objective infinite programming using the theory of abstract optimization problems in infinite dimensional spaces we provide necessary optimality conditions of first and second order for weakly efficient solutions of the multi objective infinite programming problem sufficient conditions are given under invexity assumptions we generalize the notion of kkt invexity for the multi objective infinite problem and show that this notion is a necessary and sufficient condition for every vector kkt solution to be a weakly efficient solution moreover we develop a theorem of the alternative useful for proving some of our results

generalized proper efficiency and duality for a class of nondifferentiable multiobjective variational problems withv invexity abstract a mond weir type dual for a class of nondifferentiable multiobjective variational problems in which every component of the objective function contains a term involving the square root of a certain positive semidefinite quadratic form is considered and various duality results viz weak strong and converse duality theorems are developed for conditionally properly efficient solutions these results are obtained under v invexity assumptions and its generalizations on objective and constraint functions this work extends many results on variational problems established earlier

multiobjective programming under d invexity abstract in this paper a generalization of convexity is considered in the case of nonlinear multiobjective programming problem where the functions involved are nondifferentiable by considering the concept of pareto optimal solution and substituting d invexity for convexity the fritz john type and karush kuhn tucker type necessary optimality conditions and duality in the sense of mond weir and wolfe for nondifferentiable multiobjective programming are given

solitary wave solutions to the generalized coupled mkdv equation with multi component using the darboux matrix method the multi solitary wave solutions of the generalized coupled mkdv equation with multi component are obtained the obtained solution formulas provide us with a comprehensive approach to construct exact solutions for the generalized coupled mkdv equation by some basic solutions of the boiti and tu spectral problem

solitons backlund transformation and lax pair for the 2 1 dimensional boiti leon pempinelli equation for the water waves under investigation in this paper is the 2 1 dimensional boiti leon pempinelli blp equation for the water waves by virtue of the binary bell polynomials and symbolic computation the bilinear form for the blp equation is obtained furthermore soliton solutions are presented and soliton interaction properties including the elastic inelastic and elastic inelastic collisions are discussed by the graphical analysis besides the backlund transformation in the form of the binary bell polynomials is derived via the backlund transformation the shock wave solutions and lax pair are both constructed

monotone waveform relaxation for systems of nonlinear differential algebraic equations we present a monotone waveform relaxation algorithm which produces very tight upper and lower bounds of the transient response of a class of systems described by nonlinear differential algebraic equations daes that satisfy certain lipschitz conditions the choice of initial iteration is critical and we give two methods of finding it we show that the class of systems in which monotone convergence of waveform relaxation is possible is actually larger than previously reported numerical experiments are given to confirm the monotonicity of convergence of the algorithm

n soliton solutions for the 2 1 dimensional hirota maccari equation in fluids plasmas and optical fibers abstract under investigation in this paper is the hirota maccari equation which is a generalized 2 1 dimensional model in fluid dynamics plasma physics and optical fiber communication with the aid of the hirota bilinear method and symbolic computation the corresponding n soliton solutions are given and illustrated the characteristic face method and asymptotic analysis are applied to discuss the solitonic propagation and collision including the bidirectional solitons elastic interactions and inelastic interactions finally a kind of special phenomenon with the parameters varying is investigated which might provide people with useful information on the dynamics of the relevant fields

the gap function for optimization problems in banach spaces abstract in this paper some properties of the gap function for multiple objective optimization problems in banach spaces are established

pre invex functions in multiple objective optimization and called such functions convexlike if s is a convex set and if f is a convex function then clearly f is convexlike elster and nehse obtained a saddlepoint optimality condition for convexlike mathematical programs hayashi and komiya 9 also considered convexlike functions and developed a gordan type theorem of the alternative involving convexlike functions and in addition considered lagrangian duality for convexlike programs hanson 7 considered differentiable functions f s r for which there exists an n dimensional vector function q q u such that for all x u e s

a jacobi waveform relaxation method for odes a jacobi waveform relaxation wr method for solving initial value problems for ordinary differential equations odes is presented in each window the method uses a technique called dynamic fitting and a pair of continuous runge kutta rk formulas to produce the initial waveform after which a fixed number of waveform iterates are computed the reliability and efficacy of the method are demonstrated numerically by applying it to qualitatively different problems for linear tridiagonal odes

solitonic propagation and interaction for a generalized variable coefficient forced korteweg de vries equation in fluids under investigation is a generalized variable coefficient forced korteweg de vries equation in fluids and other fields from the bilinear form of such equation the n soliton solution and a type of analytic solution are constructed with symbolic computation analytic analysis indicates that 1 dispersive and dissipative coefficients affect the solitonic velocity 2 external force term affects the solitonic velocity and background 3 line damping coefficient and some parameters affect the solitonic velocity background and amplitude solitonic propagation and interaction can be regarded as the combination of the effects of various variable coefficients according to a constraint among the nonlinear dispersive and line damping coefficients in this paper the possible applications of our results in the real world are also discussed in three aspects i e solution with the constraint solution without the constraint and approximate solution

soliton solutions and a backlund transformation for a generalized nonlinear schrodinger equation with variable coefficients from optical fiber communications under investigation in this paper is a generalized nonlinear schrodinger model with variable dispersion nonlinearity and gain loss which could describe the propagation of optical pulse in inhomogeneous fiber systems by employing the hirota method one and two soliton solutions are obtained with the aid of symbolic computation furthermore a general formula which denotes multi soliton solutions is given some main properties of the solutions are discussed simultaneously as one important property of nonlinear evolution equation the backlund transformation in bilinear form is also constructed which is helpful on future research and as far as we know is firstly proposed in this paper

optical solitons in a monomode fiber we discuss the propagation of optical solitons in a monomode fiber as a model of long distance high bit rate transmission system we give several new results which did not appear in our previous papers on this subject such as 1 a derivation of the perturbed nonlinear schrodinger equation from the maxwell equation 2 on the integrability of the perturbed nonlinear schrodinger equation 3 a discussion of the soliton as a stable fixed point of certain infinite dimensional map generated by a transmission system with periodic excitations

painleve property soliton like solutions and complexitons for a coupled variable coefficient modified korteweg de vries system in a two layer fluid model abstract as a model derived from a two layer fluid system which describes the atmospheric and oceanic phenomena a coupled variable coefficient modified korteweg de vries system is concerned in this paper with the help of symbolic computation its integrability in the painleve sense is investigated furthermore hirota s bilinear method is employed to construct the bilinear forms through the dependent variable transformations and soliton like solutions and complexitons are derived finally effects of variable coefficients are discussed graphically and it is concluded that the variable coefficients control the propagation trajectories of solitons and complexitons