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

a new extended tanh function method and its application to the dispersive long wave equations in 2 1 dimensions in this paper a new extended tanh function method is suggested to constructing multiple exact solutions for nonlinear partial differential equations the validity and reliability of the method is tested by its application to the dispersive long wave equations in 2 1 dimensions more new explicit exact solutions are found

ergodic primal convergence in dual subgradient schemes for convex programming lagrangean dualization and subgradient optimization techniques are frequently used within the field of computational optimization for finding approximate solutions to large structured optimization prob lems the dual subgradient scheme does not automatically produce primal feasible solutions there is an abundance of techniques for computing such solutions via penalty functions tangential approximation schemes or the solution of auxiliary primal programs all of which require a fair amount of computational effort we consider a subgradient optimization scheme applied to a lagrangean dual formulation of a convex program and construct at minor cost an ergodic sequence of subproblem solutions which converges to the primal solution set numerical experiments performed on a traffic equilibrium assignment problem under road pricing show that the computation of the ergodic sequence results in a considerable improvement in the quality of the primal solutions obtained compared to those generated in the basic subgradient scheme

least norm linear programming solution as an unconstrained minimization problem abstract it is shown that the dual of the problem of minimizing the 2 norm of the primal and dual optimal variables and slacks of a linear program can be transformed into an unconstrained minimization of a convex parameter free globally differentiable piecewise quadratic function with a lipschitz continuous gradient if the slacks are not included in the norm minimization one obtains a minimization problem with a convex parameter free quadratic objective function subject to nonnegativity constraints only

new multiple soliton like solutions to the generalized 2 1 dimensional kp equation a new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations pdes in a unified way the main idea of this method is to take full advantage of the riccati equation which has more new solutions more new multiple soliton like solutions are obtained for the the generalized 2 1 dimensional kp equation

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

exact solutions to nonlinear schrodinger equation with variable coefficients abstract according to ma fuchsseiter s idea a trial equation method was proposed to find the exact envelop traveling wave solutions to some nonlinear differential equations with variable coefficients as an application combining with the complete discrimination system for polynomial some exact envelop traveling wave solutions to schrodinger equation with variable coefficients were obtained at the same time the physical meanings of the obtained solutions are discussed and the problem needed to further study is pointed out

explicit exact solutions for new general two dimensional kdv type and two dimensional kdv burgers type equations with nonlinear terms of any order in this paper we have improved the tanh method by means of a proper transformation and a general ansatz applying the improved method and direct assumption method with symbolic computation we consider two kinds of equations general two dimensional kdv type equations with nonlinear terms

exact solutions to the two dimensional korteweg de vries burgers equation two methods are described for obtaining exact travelling monotone shock wave solutions to the two dimensional korteweg de vries burgers equation they are compared with two methods that have been reported recently by other authors

convergence criteria for systems of non linear elliptic boundary value partial differential equations abstract this paper deals with convergence criteria for a special system of non linear elliptic boundary value partial differential equations a fixed point algorithm is used which iteratively solves one linearized elliptic partial differential equation at a time we establish conditions which help predict the convergence of the fixed point algorithm we prove under reasonable hypotheses that the algorithm converges experimental results are reported which show that algorithm converges in wide variety of cases and the convergence is well correlated with the theoretical conditions introduced in this paper

exact travelling wave solutions of nonlinear evolution equation of surface waves in a convecting fluid exact travelling wave solutions in terms of the weierstrass p function of the equation eta t a0 eta x a1 eta eta x a2 eta xxx b0 eta xx b 1 eta eta x x b2 eta xxxx 0 are obtained these solutions may describe particularly both the evolution of a bounded conoidal wave and kink shaped waves

travelling wave solutions and proper solutions to the two dimensional burgers korteweg de vries equation in this paper we study the two dimensional burgers korteweg de vries 2d bkdv equation by analysing an equivalent two dimensional autonomous system which indicates that under some particular conditions the 2d bkdv equation has a unique bounded travelling wave solution then by using a direct method a travelling solitary wave solution to the 2d bkdv equation is expressed explicitly which appears to be more efficient than the existing methods proposed in the literature at the end of the paper the asymptotic behaviour of the proper solutions of the 2d bkdv equation is established by applying the qualitative theory of differential equations

exact solutions of some systems of nonlinear partial differential equations using symbolic computation abstract in this paper we present a solution method that utilizes symbolic computation to obtain exact traveling wave solutions of some systems of nonlinear partial differential equations the solution method is demonstrated by obtaining solutions to the variant shallow water wave equations

a family of exact travelling wave solutions to nonlinear evolution and wave equations a family q of the multicomponent special functions is defined for obtaining the exact travelling wave solutions to nonlinear evolution and wave equations it is shown that the functions qn from q for some n 2 4 are closely related to the special unitary groups su n the necessary and sufficient conditions for existence of a family of the exact multicomponent travelling wave solutions to a quasilinear evolution equation are given an efficiency of the method based on q functions is demonstrated on several classes of the nonlinear partial differential equations

exact solutions of one pattern formation model abstract the nonlinear evolution equation for describing the pattern formation processes on the semiconductor surfaces under ion beam bombardment is studied the painleve analysis of equation is considered the new elliptic solution of this equation is obtained

algorithm and mechanization to cauchy problem of wave equation with linear damping and source terms this paper discusses the cauchy problem of wave equation with linear damping and source terms the author reduces the problem to a parabolic one and uses the corresponding initial value to construct the solutions of the resulting parabolic problem thereafter he obtains a brief algorithmization formula to this problem with mechanization in maple

travelling wave solutions to the korteweg de vries burgers equation the existence and certain qualitative properties of travelling wave solutions to the korteweg de vries burgers equation are established the limiting behaviour of these waves when e tends to zero and when tends to zero is examined together with a singular limit wherein both e and tend to zero

symmetries and invariant solutions of the two dimensional variable coefficient burgers equation we discuss symmetries and reductions of the two dimensional burgers equation with variable coefficient we classify one dimensional and two dimensional subalgebras of the burgers symmetry algebra which is infinite dimensional into conjugacy classes under the adjoint action of the symmetry group invariance under one dimensional subalgebras provides reductions to lower dimensional partial differential equations further reductions of these equations to second order ordinary differential equations are obtained through invariance under two dimensional subalgebras the reduced odes are then analysed and shown that they belong to the polynomial class of second order equations which can be linearized only for particular values of parameters figuring in the coefficient

exact periodic solutions of the complex ginzburg landau equation three new exact periodic solutions of the complex ginzburg landau equation are obtained in terms of the weierstrass elliptic function furthermore the new periodic solutions and other shock solutions appear as their bounded limits along the real axis for particular relationships between the coefficients in the equation in the general case bounded limits are nothing but the already known pulse hole and shock solutions it is also shown that the shapes of the solutions are quite different from the shape of the usual envelope wave solution in particular the spatial structure of the new bounded periodic solutions varies in time while the pulse solution may exhibit breather like behavior

generalized tanh method with symbolic computation and generalized shallow water wave equation abstract we report that symbolic computation with the generalized tanh method leads to new soliton like solutions for a 2 1 dimensional generalization of the shallow water wave equations

new travelling wave solutions to the ostrovsky equation in this work new travelling wave solutions to the ostrovsky equation are studied by employing the improved tanh function method with this method the ostrovsky equation is reduced to the nonlinear ordinary differential equation and then the different types of exact solutions are derived based on the solutions of the riccati equation we will compare our solutions with those gained by the other methods

an exact solution to two dimensional korteweg de vries burgers equation by applying a special solution of square hopf cole type to an ordinary differential equation the authors propose a bounded travelling wave solution u x y t v xi v kx ly omega t to the two dimensional korteweg de vries burgers equation which is monotonic and possesses an inflection point with respect with xi

soliton solutions and doubly periodic wave solutions for a new generalized hirota satsuma coupled system in this paper a new algebraic method with symbolic computation is presented to uniformly construct a series of exact solutions for general nonlinear equations compared with most existing tanh 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 for illustration we apply the proposed method to solve a new generalized hirota satsuma coupled system and explicitly construct a series of exact solutions which include the soliton solutions and elliptic doubly periodic solutions as special cases in addition the links among our proposed method the tanh method and the extended method are also clarified generally

observations on the tanh coth expansion method for finding solutions to nonlinear evolution equations abstract the tanh coth expansion method for finding solitary travelling wave solutions to nonlinear evolution equations has been used extensively in the literature it is a natural extension to the basic tanh function expansion method which was developed in the 1990s it usually delivers three types of solution namely a tanh function expansion a coth function expansion and a tanh coth expansion it is known that for every tanh function expansion solution there is a corresponding coth function expansion solution it is shown that there is a tanh coth expansion solution that is merely a disguised version of the coth solution in many papers such tanh coth solutions are erroneously claimed to be new however other tanh coth solutions may be delivered that are genuinely new in the sense that they would not be delivered via the basic tanh function method similar remarks apply to tan cot and tan cot expansion solutions

iterative solution of linear programs by perturbing a linear program to a quadratic program it is possible to solve the latter in its dual variable space by iterative techniques such as successive over relaxation sor methods this provides a solution to the original linear program

application of the kudryashov method for finding exact solutions of the high order nonlinear evolution equations abstract the application of the kudryashov method for finding exact solutions of the high order nonlinear evolution equations is considered some classes of solitary wave solutions for the families of nonlinear evolution equations of fifth sixth and seventh order are obtained the efficiency of the kudryashov method for finding exact solutions of the high order nonlinear evolution equations is demonstrated

traveling wave solutions for nonlinear equations using symbolic computation abstract in this paper a direct and unified algorithm for constructing multiple travelling wave solutions of nonlinear partial differential equations pdes is presented and implemented in a computer algebraic system the key idea of this method is to take full advantage of a riccati equation involving a parameter and use its solutions to replace the tanh function in the tanh method it is quite interesting that the sign of the parameter can be used to exactly judge the number and types of such travelling wave solutions in this way we can successfully recover the previously known solitary wave solutions that had been found by the tanh method and other more sophisticated methods more importantly for some equations with no extra effect we also find other new and more general solutions at the same time by introducing appropriate transformations our method is further extended to the nonlinear pdes whose balancing numbers may be any nonzero real numbers the efficiency of the method can be demonstrated on a large variety of nonlinear pdes such as those considered in this paper burgers huxley equation coupled korteweg de vries equation caudrey dodd gibbon kawada equation active dissipative dispersive media equation generalized fisher equation and nonlinear heat conduction equation

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

an iterative aggregation procedure for markov decision processes an iterative aggregation procedure is described for solving large scale finite state finite action markov decision processes mdps at each iteration an aggregate master problem and a sequence of smaller subproblems are solved the weights used to form the aggregate master problem are based on the estimates from the previous iteration each subproblem is a finite state finite action mdp with a reduced state space and unequal row sums global convergence of the algorithm is proven under very weak assumptions the proof relates this technique to other iterative methods that have been suggested for general linear programs

applications of the combined tanh function method with symmetry method to the nonlinear evolution equations based on the symbolic computation we combined the tanh function method with the symmetry method to construct new type of solutions of the nonlinear evolution equations for the first time with the combined method some new types of solutions of the coupled 2 1 dimensional nonlinear system of schrodinger equations were obtained and their properties were studied by analyzing their figures

elliptic equation s new solutions and their applications to two nonlinear partial differential equations abstract in the present paper with the aid of symbolic computation families of new nontrivial solutions of first order elliptic equation 2 a 0 a 1 a 2 2 a 3 3 a 4 4 where d d x are obtained to our knowledge these nontrivial solutions can not be found in chaos solitons fract 26 2005 785 794 and phys lett a 336 2005 463 476 by yomba and other existent papers until now by using these nontrivial solutions a direct algebraic method is described to construct several kinds of exact non travelling wave solutions for the 2 1 dimensional breaking soliton equations and the 2 1 dimensional asymmetric nizhnik novikov vesselov equation by using this method many other physically important nonlinear partial differential equations nlpdes can be investigated and new non travelling wave solutions can be explicitly obtained with the aid of symbolic computation system maple

a numerical algorithm for hydrodynamic free boundary problems a generalized formulation of inviscid incompressible hydrodynamics as a system of conservation laws subject to a one sided density constraint is used as the basis of a numerical algorithm for a variety of hydrodynamic free surface problems benchmark calculations for colliding masses of fluid and for the motion of a spherically symmetric bubble are compared with theoretical predictions also shown are profiles calculated for an evolving underwater bubble near a wall energy dissipation is introduced as a measure of turbulence and is used in analyzing the numerical results convergence behavior of the numerical algorithm is discussed

korteweg de vries burgers equation and the painleve property it is shown that the korteweg de vries burgers equation possesses the painleve property conditionally using an algorithmic approach a travelling wave solution is reproduced

weierstrass traveling wave solutions for dissipative benjamin bona and mahony bbm equation in this paper the effect of a small dissipation on waves is included to find exact solutions to the modified benjamin bona and mahony bbm equation by viscosity using lyapunov functions and dynamical systems theory we prove that when viscosity is added to the bbm equation in certain regions there still exist bounded traveling wave solutions in the form of solitary waves periodic and elliptic functions by using the canonical form of abel equation the polynomial appell invariant makes the equation integrable in terms of weierstrass functions we will use a general formalism based on ince s transformation to write the general solution of dissipative bbm in terms of functions from which all the other known solutions can be obtained via simplifying assumptions using ode ordinary differential equations analysis we show that the traveling wave speed is a bifurcation parameter that makes transition between different classes of waves

the tanh method a tool for solving certain classes of nonlinear evolution and wave equations the tanh or hyperbolic tangent method is a powerful technique to search for travelling waves coming out from one dimensional nonlinear wave and evolution equations in particular in those problems where dispersive effects reaction diffusion and or convection play an important role to show the strength of the method an overview is given to find out which kind of problems are solved with this technique and how in some nontrivial cases this method adapted to the problem at hand still can be applied single as well as coupled equations arising from wave phenomena which appear in different scientific domains such as physics chemical kinetics geochemistry and mathematical biology will be treated next attention is focussed towards approximate solutions as a result solitary and shock wave profiles are derived together with the associated width and velocity the same method can be easily extended so that difference differential equations can be similarly solved finally some extensions of the method are discussed

a row relaxation method for large l1 problems abstract this paper presents a row relaxation method for solving the regularized l 1 problem minimize 1 2 e x 2 2 a x b 1 it is shown that the dual of this problem has the form minimize 1 2 a t y 2 2 e b t y subject to y 1 and if y solves the dual then a t y e solves the primal the fact that the dual variables have simple bounds enables us to apply a wide range of methods the method derived in this paper is a row relaxation method that resembles kaczmarz s method this feature makes it suitable for solving problems in which a is large sparse and unstructured another advantage is that the method is easily adapted to handle linear constraints the paper introduces an iterative improvement technique that shifts the limit of the iterative process toward a solution of the unregularized problem minimize a x b 1

a rational generalization of fan s method and its application to generalized shallow water wave equations in this paper we employ a rational expansion to generalize fan s method for exact travelling wave solutions for nonlinear partial differential equations pdes to verify the reliability of the proposed method the generalized shallow water wave gsww equation has been investigated as an example kinds of new exact travelling wave solutions of a rational form have been obtained this indicates that the proposed method provides a more general result for exact solution of nonlinear equations

an application of the decompositionmethod for the two dimensional kdv burgers equation a relatively new decomposition method is presented to find the explicit and numerical solutions of the two dimensional korteweg de vries burgers equation tdkdvb for short for the initial conditions some numerical results are also given for this equation by using the decomposition method

periodic solutions of the non integrable convective fluid equation in the present paper we have obtained and analyzed a family of exact periodic solutions of the nonlinear evolution partial differential convecting fluid equation cfe by applying a modification of the bilinear transformation method this modification is used in view of the circumstance that cfe is a non integrable nonlinear equation a detailed consideration has been given to the quite important case of balance between the dispersion and nonlinear effects establishing that this balance changes the structure of the equation itself the exact periodic solutions of cfe have been also found in the important case when cfe is identical with the kuramoto sivashinsky equation

on multilevel iterative methods for optimization problems this paper is concerned with multilevel iterative methods which combine a descent scheme with a hierarchy of auxiliary problems in lower dimensional subspaces the construction of auxiliary problems as well as applications to elasto plastic model and linear programming are described the auxiliary problem for the dual of a perturbed linear program is interpreted as a dual of perturbed aggregated linear program coercivity of the objective function over the feasible set is sufficient for the boundedness of the iterates equivalents of this condition are presented in special cases

locating the least 2 norm solution of linear programs via a path following method a linear program has a unique least 2 norm solution provided that the linear program has a solution to locate this solution most of the existing methods were devised to solve certain equivalent perturbed quadratic programs or unconstrained minimization problems we provide in this paper a new theory which is different from these traditional methods and is an effective numerical method for seeking the least 2 norm solution of a linear program the essence of this method is a interior point like path following algorithm that traces a newly introduced regularized central path that is fairly different from the central path used in interior point methods one distinguishing feature of our method is that it imposes no assumption on the problem the iterates generated by this algorithm converge to the least 2 norm solution whenever the linear program is solvable otherwise the iterates converge to a point which gives a minimal kkt residual when the linear program is unsolvable

nonlinear periodic solutions for isothermal magnetostatic atmospheres the equations of magnetohydrostatic equilibria for a plasma in a gravitational field are investigated analytically for equilibria with one ignorable spatial coordinate the equations reduce to a single nonlinear elliptic equation for the magnetic potential known as the grad shafranov equation specifying the arbitrary function in the latter equation yields a nonlinear elliptic equation analytical nonlinear periodic solutions of this elliptic equation are obtained for the case of an isothermal atmosphere in a uniform gravitational field e g a model for the solar atmosphere we obtained several classes of exact solutions of five nonlinear evolution equations liouville sinh poisson double sinh poisson sine poisson and double sine poisson using the generalized tanh method moreover the backlund transformations are used to generate further new classes of solutions the final results may be used to investigate some models in solar physics

a dual differentiable exact penalty function a new penalty function is associated with an inequality constrained nonlinear programming problem via its dual this penalty function is globally differentiable if the functions defining the original problem are twice globally differentiable in addition the penalty parameter remains finite this approach reduces the original problem to a simple problem of maximizing a globally differentiable function on the product space of a euclidean space and the nonnegative orthant of another euclidean space many efficient algorithms exist for solving this problem for the case of quadratic programming the penalty function problem can be solved effectively by successive overrelaxation sor methods which can handle huge problems while preserving sparsity features

exact solutions of systems describing interacting populations with low critical densities the generalization of the simplest equation method to look for exact solutions of systems of nonlinear differential equations is presented the exact solutions of nde systems describing the evolution of two interacting populations in two cases both populations have the low critical density or low critical density is typical for only one of populations are obtained

travelling wave solutions to the two dimensional kdv burgers equation travelling wave solutions for the two dimensional kdv burgers equation are obtained by using mathematica they are shown to be sums of a shock wave and solitary wave

algorithmization formula and mechanization to cauchy problem of high dimensional wave equation this paper discusses the constructive method and mechanization to the cauchy problem of high dimensional wave equations the author uses the initial value to construct the solutions that satisfy the initial conditions and obtain a brief algorithmization formula to this problem thereafter the algorithmization formula is used in maple to solve this cauchy problem automatically

the adventures of a simple algorithm abstract this paper presents analyzes and tests a row action method for solving the regularized linear programming problem minimize 1 2 x 2 2 c t x subject to a x b where is a given positive constant the proposed method is based on the observation that the dual of this problem has the form maximize b t y 1 2 a t y c 2 2 subject to y 0 and if y solves the dual then the point x a t y c provides the unique solution of the primal maximizing the dual objective function by changing one variable at a time results in an effective row action method which is suitable for solving large sparse problems one aim of this paper is to clarify the convergence properties of the proposed scheme let y k denote the estimated dual solution at the end of the k th iteration and let x k a t y k c denote the corresponding primal estimate it is proved that the sequence x k converges to x while the sequence y k converges to a point y that solves the dual the only assumption which is needed in order to establish these claims is that the feasible region is not empty yet perhaps the more striking features of the algorithm are related to temporary situations in which it attempts to solve an inconsistent system in such cases the sequence y k obeys the rule y k u k k v where u k is a fastly converging sequence and v is a fixed vector that satisfies a t v 0 and b t v 0 so the sequence x k is almost unchanged for many iterations the paper ends with numerical experiments that illustrate the effects of this phenomenon and the close links with kaczmarz s sor method

explicit traveling wave solutions of five kinds of nonlinear evolution equations abstract first of all by using bernoulli equations we develop some technical lemmas then we establish the explicit traveling wave solutions of five kinds of nonlinear evolution equations nonlinear convection diffusion equations including burgers equations nonlinear dispersive wave equations including korteweg de vries equations nonlinear dissipative dispersive wave equations including ginzburg landau equation korteweg de vries burgers equation and benjamin bona mahony burgers equation nonlinear hyperbolic equations including sine gordon equation and nonlinear reaction diffusion equations including belousov zhabotinskii system of reaction diffusion equations

exact solitary waves in a convecting fluid the perturbed korteweg de vries equation ut lambda 1uux lambda 2uxxx lambda 3uxxxx lambda 4 uux x lambda 5uxx 0 which describes the evolution of long shallow waves in a convecting fluid when the critical rayleigh number slightly exceeds its critical value admits two types of exact solitary wave solution

stability of pseudospectral and finite difference methods for variable coefficient problems it is shown that pseudospectral approximation to a special class of variable coefficient one dimensional wave equations is stable and convergent even though the wave speed changes sign within the domain computer experiments indicate similar results are valid for more general problems similarly computer results indicate that the leapfrog finite difference scheme is stable even though the wave speed changes sign within the domain however both schemes can be asymptotically unstable in time when a fixed spatial mesh is used

elliptic solutions of the quintic complex one dimensional ginzburg landau equation the conte musette method has been modified for the search of only elliptic solutions to systems of differential equations a key idea of this a prior restriction is to simplify calculations by means of the use of a few laurent series solutions instead of one and the use of the residue theorem the application of this approach to the quintic complex one dimensional ginzburg landau equation cgle5 allows us to find elliptic solutions in the wave form restrictions on coefficients which are necessary conditions for the existence of elliptic solutions for the cgle5 have been found as well we demonstrate that to find elliptic solutions the analysis of a system of differential equations is preferable to the analysis of the equivalent single differential equation

stable galerkin methods for hyperbolic systems this paper considers the stability of the galerkin method for first order hyperbolic systems just as in finite difference theory many galerkin methods stable and convergent for the cauchy problem are unstable for hyperbolic boundary value problems because of improper treatment of the boundary conditions the usual galerkin method is seen to be unstable for a linear constant coefficient well posed hyperbolic system on 0 1 a method of treating boundary conditions is then proposed which will yield a stable and convergent method for any well posed linear hyperbolic system in one dimension this idea generalizes in a natural way to problems in more than one space dimension examples in one and two dimensions are considered this paper extends the work of gunzburger math comp 31 1977 pp 671 675 to the general hyperbolic system

newton s method for linear inequality systems abstract we describe a modified newton type algorithm for the solution of linear inequality systems in the sense of minimizing the l 2 norm of infeasibilities finite termination is proved and numerical results are given

analytic study on two nonlinear evolution equations by using the g g expansion method abstract the validity and reliability of the so called g g expansion method is tested by applying it to two nonlinear evolutionary equations solutions in more general forms are obtained when the parameters are taken as special values it is observed that the previously known solutions can be recovered new rational function solutions are also presented being concise and less restrictive the method can be applied to many nonlinear partial differential equations

painleve analysis and backlund transformation in the kuramoto sivashinsky equation the authors apply the painleve test to the kuramoto sivashinsky nonlinear partial differential equation which describes many interesting fluid motions the equation passes the test in a weak sense although the painleve analysis does not yield the general solution they perform the backlund transformation in order to obtain new particular solutions the authors find explicitly all the solutions of the set of equations which define the painleve backlund transformation they reduce to only one type namely the already known kink shaped solitary wave