hyponormality of toeplitz operators on the weighted bergman space with matrix valued circulant symbols abstract in this paper we consider the hyponormality of toeplitz operators t on the weighted bergman space with matrix valued circulant symbols we give a necessary and sufficient condition for the hyponormality of t with such a symbol under some constraint on the entries of the matrix

the periodic boundary value problem for semilinear elastic beam equations the resonance case this paper discusses the existence of generalized solutions to periodic boundary value problems for semilinear elastic beam equations under a resonance condition the argument presented makes use of the global inverse theorem and galerkin s method

least squares quadratic b spline finite element method for the regularised long wave equation abstract an approximate solution consisting of a combination of the quadratic b spline functions is incorporated into the least squares method an application of this method is presented for computing the solution of the regularised long wave rlw equation quadratic b spline solution of the rlw equation leads to tridiagonal matrix system which is solved easily by using the thomas algorithm performance of this scheme is tested by obtaining a solitary wave solution of the equation and by studying the development of the undular bore numerical results of the proposed algorithm is shown to have higher accuracy in terms of l 2 error norm compared studying the migration of the solitary wave a fourier stability analysis of the method is investigated

collocation solution for rlw equation with septic spline a collocation solution using the septic splines as a shape function for the regularized long wave rlw equation is presented here a linear stability analysis shows the scheme to be unconditionally stable test problems which migration and interaction of solitary waves are used to validate our scheme by calculate l 2 norm and l norm and three invariants of motion are evaluates to determine the conservation properties of the algorithm the numerical scheme is compared with other published methods and shown to be accurate and efficient

error propagation when approximating multi solitons the kdv equation as a case study abstract the paper studies the influence of the time discretizations when simulating some phenomena involving more than one solitary wave taking the kdv equation as a case study we obtain some conditions on the numerical method in order to get a more correct simulation of multi soliton solutions they are related to the evolution of the conserved quantities of the problem through the numerical integration it is shown that when approximating n solitons a method that preserves n invariants of the problem shows a better time propagation of the error than that of a general scheme as a consequence of this the simulation of some physical parameters that characterize the waves is more suitable when using conservative integrators we also show how these results can be extended to the approximation to multi solitons of any equation of the kdv hierarchy and more generally other integrable equations

free vibrations for a semilinear wave equation abstract existence and regularity of nontrivial time periodic solutions are proved for semilinear wave equations under mild smoothness monotonicity and superlinearity assumptions the forced vibration case is also treated

a two dimensional bi cubic b spline finite element used in a study of mhd duct flow abstract a two dimensional bi cubic b spline finite element is proposed and used within a galerkin approach to model magneto hydrodynamic duct flow excellent agreement is obtained between the numerical results and the analytic solution even for large values of the applied magnetic field

application of galerkin s method to equal width wave equation the non linear equal width equation is solved by galerkin s method using linear finite elements a linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found employing the crank nicolson approach including a product approximation the three invariants of the motion are calculated to determine the conservation properties of the system l 2 and l error norms are used to measure differences between the exact and numerical solutions the simulations of solitary wave motion are used to determine the properties of the algorithm finally the development of an undular bore is studied

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

hyponormal toeplitz operators and extremal problems of hardy spaces the symbols of hyponormal toeplitz operators are completely described and those are also studied being related with the extremal problems of hardy spaces moreover we discuss halmos s question about a subnormal toeplitz operator when the self commutator is finite rank

solitary wave solutions of the grlw equation using septic b spline collocation method in this work solitary wave solutions of the generalized regularized long wave grlw equation are obtained by using septic b spline collocation method with two different linearization techniques to demonstrate the accuracy and efficiency of the numerical scheme three test problems are studied by calculating the error norms l2 and l and the invariants i1 i2 and i3 a linear stability analysis based on the von neumann method of the numerical scheme is also investigated consequently our findings indicate that our numerical scheme is preferable to some recent numerical schemes

hermite infinite elements and graded quadratic b spline finite elements quadratic b spline finite elements are defined for a graded mesh hermite infinite elements are proposed to extend the applicability of these finite elements to unbounded regions test problems used to compare this technique with published procedures show that the quadratic b spline finite element solution has as expected lower error bounds than a linear element solution these experiments also demonstrate that the hermite infinite elements used to close the b spline finite element arrays lead to error norms comparable in size with other infinite element formulations the generation of solitary waves in a semi infinite shallow channel by boundary forcing is modelled by the korteweg de vries equation using an array of graded elements closed by a zero pole infinite element the resulting simulation of solitary wave motion across a non uniform mesh confirms existing work and illustrates the effectiveness of the present formulation

numerical solitons of generalized korteweg de vries equations abstract we propose a numerical method for finding solitary wave solutions of generalized korteweg de vries equations by solving the nonlinear eigenvalue problem on an unbounded domain the artificial boundary conditions are obtained to make the domain finite we specially discuss the soliton solutions of the k m n equation and kdv k m n equation furthermore for the mixed models of linear and nonlinear dispersion the collision behaviors of soliton soliton and soliton antisoliton are observed

mixed finite element analysis and numerical solitary solution for the rlw equation in this paper a mixed finite element mfe formulation is proposed for the 1 d regularized long wave rlw equation u t auu x delta u xxt 0 the existence of its mixed generalized solution and semidiscrete and fully discrete mixed finite element solutions is proved error estimates based on energy methods are given and finally results of numerical experiments comparing this formulation with a galerkin method based on cubic splines are also given

synchronization of coupled self excited elastic beams abstract the behavior of four coupled self excited elastic beams is numerically studied using the finite difference method self excitation is modeled by adding a van der pol damping term coupling based on shared boundary conditions at the roots of the beams is proposed and the influence of the coupling on the dynamics is analyzed time and space correlation coefficients are employed to measure the degree of synchronization among beams through the power spectral density multiple frequencies of the beam tip time series are determined unveiling the complex nature of the beam motions finally the robustness of the proposed behavior to changes in fluid structure interaction and the mass of the beams is determined

solitary waves of the regularized long wave equation abstract a finite element solution of the regularised long wave equation based on galerkin s method using cubic splines as element shape functions is set up a linear stability analysis shows the scheme to be unconditionally stable test problems including the migration and interaction of solitary waves are used to validate the method which is found to be accurate and efficient the three invariants of the motion are evaluated to determine the conservation properties of the algorithm the temporal evolution of a maxwellian initial pulse is then studied

absorbing boundary conditions for the stationary forced kdv equation abstract in the present work we study the stationary korteweg de vries kdv equation with a forcing for a flow of an inviscid and incompressible fluid the stationary fkdv equation is defined in an infinite domain and it is reduced to a bounded domain by introducing absorbing boundary conditions a new numerical method is proposed to solve this boundary value problem new multiple numerical solitary wave solutions of the stationary kdv equation are discussed for various forcings numerical examples are provided to confirm and illustrate the accuracy and effectiveness of the method

superconvergence of a finite element approximation to the solution of a sobolev equation in a single space variable a standard galerkin method for a quasilinear equation of sobolev type using continuous piecewise polynomial spaces is presented and analyzed optimal order error estimates are established in various norms and nodal superconvergence is demonstrated discretization in time by explicit single step methods is discussed

solitary waves of the equal width wave equation a numerical solution of the equal width wave equation based on galerkin s method using cubic b spline finite elements is used to simulate the migration and interaction of solitary waves the interaction of two solitary waves is seen to cause the creation of a source for solitary waves usually these are of small magnitude but when the amplitudes of the two interacting waves are equal and opposite the source produces trains of solitary waves whose amplitudes are of the same order as those of the initiating waves the three invariants of the motion are evaluated to determine the conservation properties of the system finally the temporal evolution of a maxwellian initial pulse is studied for small ut uux uxxt 0 only positive waves are formed and the behaviour mimics that of the kdv and filw equations for larger values of d both positive and negative solitary waves are generated

a collocation method with cubic b splines for solving the mrlw equation the modified regularized long wave mrlw equation is solved numerically by collocation method using cubic b splines finite element a linear stability analysis of the scheme is shown to be marginally stable three invariants of motion are evaluated to determine the conservation properties of the algorithm also the numerical scheme leads to accurate and efficient results moreover interaction of two and three solitary waves are studied through computer simulation and the development of the maxwellian initial condition into solitary waves is also shown

a new analysis of fractional drinfeld sokolov wilson model with exponential memory abstract the key purpose of this study is to suggest a new fractional extension of nonlinear drinfeld sokolov wilson dsw equation with exponential memory the nonlinear dsw equation plays a great role in describing dispersive water waves the stability analysis is executed with the aid of fixed point theory the advantage of fhatm over the other existing techniques is that its solution contains an auxiliary parameter which plays a big role in controlling the convergence of the solution the outcomes of the study are presented in the form of graphs and tables the results achieved by the use of the suggested scheme unfold that the used computational algorithm is very accurate flexible effective and simple to perform to examine the fractional order mathematical models

a gap between hyponormality and subnormality for block toeplitz operators this paper concerns a gap between hyponormality and subnormality for block toeplitz operators we show that there is no gap between 2 hyponormality and subnormality for a certain class of trigonometric block toeplitz operators e g its co analytic outer coefficient is invertible in addition we consider the extremal cases for the hyponormality of trigonometric block toeplitz operators in this case hyponormality and normality coincide

solving the generalized regularized long wave equation on the basis of a reproducing kernel space on the basis of a reproducing kernel space an iterative algorithm for solving the generalized regularized long wave equation is presented the analytical solution in the reproducing kernel space is shown in a series form and the approximate solution u n is constructed by truncating the series to n terms the convergence of u n to the analytical solution is also proved results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such evolution equations

application of the variational iteration method to the regularized long wave equation this paper applies the variational iteration method to the regularized long wave equation in this method a generalized lagrange multiplier is introduced to construct a correction functional for the discussed problem the multiplier can be identified optimally via variational theory three invariants of the motion are evaluated to determine the conservation properties of the system

soliton and antisoliton resonant interactions using the hirota formalism gibbon et al 1976 have shown that the evolution equation ut ux uxxt 4u2 2yxzt x 0 with u yt zx has the same solitary wave as the regularised long wave rlw equation ut ux uxxt 6 u2 x 0 and an exact two soliton solution describing the elastic collision of two sech2 profile solitary waves performing a more detailed analysis the authors show that the two soliton solution can also represent other processes like the resonant or the singular collision of two rlw type solitary waves the interaction type depends on the values of a characteristic parameter of the solution they also prove that with the bilinear form associated with the evolution equation a three soliton solution of the hirota type cannot exist they then study the equation ut ux uxxt 3 u2 x 6utzx 0 with u zt associated with another bilinear form which has the same solitary wave as the evolution equation they prove the existence of n soliton solutions for arbitrary n and analyse the behaviour of the solitonic solutions as in the first case the two soliton solution can describe elastic resonant or singular interaction of two rlw type solitary waves a remarkable feature of the resonant triad is that it always involves one positive and two negative waves this triad corresponds to a fundamental vertex for the analysis of the elastic soliton antisoliton interaction

petrov galerkin methods for nonlinear dispersive waves abstract petrov galerkin methods based on piecewise linear interpolants for the korteweg de vries and related equations are studied both accuracy and stability are analysed for the linearised case it is shown that in the nonlinear case the order of accuracy of the standard galerkin procedure is reduced and an alternative technique is therefore proposed which retains the fourth order accuracy in space this is found to perform well when compared with finite difference or other finite element schemes

conservative numerical methods for solitary wave interactions the purpose of this paper is to show the advantages that represent the use of numerical methods that preserve invariant quantities in the study of solitary wave interactions for the regularized long wave equation it is shown that the so called conservative methods are more appropriate to study the phenomenon and provide a dynamic point of view that allows us to estimate the changes in the parameters of the solitary waves after the collision

a boussinesq system for two way propagation of nonlinear dispersive waves abstract in this report we study the system n t w x nw x 1 6 n xxt 0 w t n x ww x 1 6 w xxt 0 which describes approximately the two dimensional propagation of surface waves in a uniform horizontal channel of length l0 filled with an irrotational incompressible inviscid fluid which in its undisturbed state has depth h the non dimensional variables n x t and w x t represent the deviation of the water surface from its undisturbed position and the horizontal velocity at water level 2 3h respectively the natural initial boundary value problem corresponding to the situation wherein the channel is fitted with a wavemaker at both ends is formulated and analyzed theoretically we then present a numerical algorithm for the approximation of solutions of the system and prove the algorithm is fourth order accurate both in time and in space is unconditionally stable and has optimal computational complexity which is to say the operation cost per time step is of order m where m is the number of grid points in the spatial discretization further we implement the algorithm as a computer code and use it to study head on collisions of solitary waves our numerical simulations are compared with existing theoretical numerical and experimental results we have tentatively concluded that the system is a good candidate for modeling two dimensional surface water waves

solitary waves induced by the boundary forced ew equation the development of a train of ew solitary waves induced by boundary forcing is studied using a petrov galerkin finite element scheme with shape functions taken as quadratic b spline functions a linear recurrence relationship for the numerical scheme is obtained via a crank nicholson approach involving a product approximation results are compared with those for the rlw and kdv equations

error estimates for galerkin finite element methods for the camassa holm equation we consider the camassa holm ch equation a nonlinear dispersive wave equation that models one way propagation of long waves of moderately small amplitude we discretize in space the periodic initial value problem for ch written in its original and in system form using the standard galerkin finite element method with smooth splines on a uniform mesh and prove optimal order l 2 error estimates for the semidiscrete approximation using the fourth order accurate explicit classical runge kutta scheme for time stepping we construct a highly accurate stable fully discrete scheme that we employ in numerical experiments to approximate solutions of ch mainly smooth travelling waves and nonsmooth solitons of the peakon type

normal singular cauchy integral operators with operator valued symbols abstract in this paper we characterize a class of normal isometric coisometric unitary hyponormal singular cauchy integral operators with operator valued or matrix valued symbols on vector valued or c n valued l 2 spaces

a decoupled and conservative difference scheme with fourth order accuracy for the symmetric regularized long wave equations in this paper a decoupled finite difference scheme with fourth order accuracy is proposed to solve the symmetric regularized long wave equation the scheme is proved to conserve the total energy in the discrete level without any restrictions on the grid ratios the convergence of the difference scheme is proved by utilizing the energy method to be of forth order in space and second order in time a numerical example is given to support the theoretical analysis

application of a lumped galerkin method to the regularized long wave equation in this paper a lumped galerkin method based on quadratic b spline finite elements is used to find numerical solutions of the one dimensional regularized long wave rlw equation with a variant of initial and boundary conditions the obtained numerical results show that the present method is a remarkably successful numerical technique for solving the equation results are compared with published numerical solutions a linear stability analysis of the scheme is also investigated

a computational method for the regularized long wave rlw equation a numerical solution of the regularized long wave rlw equation based on collocation method using cubic b spline finite elements is used to simulate the migration and interaction of solitary waves interaction of solitary waves with different amplitudes are shown the three invariants of the motion are evaluated to determine the conservation properties of the system the temporal evaluation of a maxwellian initial pulse is then studied and then we prove that the number of solitons which are generated from maxwellian initial condition are determined

conservative schemes for the symmetric regularized long wave equations in this paper we study the symmetric regularized long wave srlw equations by finite difference method we design some numerical schemes which preserve the original conservative properties for the equations the first scheme is two level and nonlinear implicit existence of its difference solutions are proved by brouwer fixed point theorem it is proved by the discrete energy method that the scheme is uniquely solvable unconditionally stable and second order convergent for u in l norm and for n in l2 norm on the basis of the priori estimates the second scheme is three level and linear implicit its stability and second order convergence are proved both of the two schemes are conservative so can be used for long time computation however they are coupled in computing so need more cpu time thus we propose another three level linear scheme which is not only conservative but also uncoupled in computation and give the numerical analysis on it numerical experiments demonstrate that the schemes are accurate and efficient

a conservative weighted finite difference scheme for regularized long wave equation in this paper a new finite difference method for initial boundary value problem of regularized long wave rlw equation is considered two energy conservative finite difference schemes are proposed and the prior estimate of the solution is obtained existence and uniqueness of numerical solution are derived it is proved that the finite difference schemes are convergent and stable numerical experiment results show that the theory is accurate and the schemes are efficient and reliable

the investigation of free vibrations for an asymmetric beam equation using category theory we investigate free vibrations for an asymmetric beam equation we find them by applying linking inequalities and the limit relative category theory

which subnormal toeplitz operators are either normal or analytic abstract we study subnormal toeplitz operators on the vector valued hardy space of the unit circle along with an appropriate reformulation of p r halmos s problem 5 which subnormal block toeplitz operators are either normal or analytic we extend and prove abrahamse s theorem to the case of matrix valued symbols that is we show that every subnormal block toeplitz operator with bounded type symbol i e a quotient of two bounded analytic functions whose analytic and co analytic parts have the left coprime factorization is normal or analytic we also prove that the left coprime factorization condition is essential finally we examine a well known conjecture of whether every subnormal toeplitz operator with finite rank self commutator is normal or analytic

a petrov galerkin method for solving the generalized regularized long wave grlw equation the generalized regularized long wave grlw equation is solved numerically by the petrov galerkin method which uses a linear hat function as the trial function and a quintic b spline function as the test function product approximation has been used in this method a linear stability analysis of the scheme shows it to be conditionally stable test problems including the single soliton and the interaction of solitons are used to validate the suggested method which is found to be accurate and efficient finally the maxwellian initial condition pulse is studied

numerical analysis of generalized regularized long wave equation using the element free kp ritz method abstract a numerical analysis of the generalized regularized long wave grlw equation by application of the element free kp ritz method is performed to approximate the displacement field an element free kernel particle estimation is employed and a system of nonlinear discrete equations is achieved by using the ritz minimization procedure to the energy expressions validation of the present numerical solutions with the exact results has been conducted by numerical examples and evidenced a good agreement

a least squares finite element scheme for the ew equation abstract the equal width ew equation is solved by a least squares technique using linear space time finite elements in simulations of the migration of a single solitary wave this algorithm is shown to have good accuracy and conservation the development of solitary waves from an arbitrary initial condition within an ew environment is examined

free vibrations for an asymmetric beam equation the existence of nontrivial solutions for the beam equations is proved in two cases the superlinearity case and the jump nonlinearity case

explicit multistep method for the numerical solution of rlw equation abstract in this paper we present explicit multistep method for regularized long wave rlw equation the discretization in space is based on the galerkin method using linear space finite elements and for the time discretization the explicit multistep method is used propagation of solitary waves and interaction of two solitary waves are simulated using the proposed method to confirm the theoretical results

b spline finite element studies of the non linear schrodinger equation abstract the non linear schrodinger equation is solved numerically by a b spline finite element method the approach used is based on collocation of cubic b splines over spatial finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range time integration of the resulting system of ordinary differential equations is effected using a crank nicolson approximation standard problems are used to validate the algorithm comparisons are made with published numerical and analytical solutions the proposed method exhibits good conservation properties and performs well the development of temporally recurrent states from spatially periodic initial conditions is examined through computer experiments the birth of mobile as well as static solitons out of maxwellian initial data is observed

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

nonlinear vibration of a beam where u cu k enexzujke jkr sinjx z and n denote the integer set and the positive integer set respectively the domain of a is given by d a u e l q iau e t q let w q be the completion of d a j under the graph norm i l4tr o l4lt2 l q then the space w2 q can be characterized by the fourier series u c ujk eik sinjx c 1 j2 lk iujk12 it is easy to see that the imbedding w12 b l q is compact c a

explicit finite difference methods for the ew and rlw equations an extensive assessment of the accuracy of explicit finite difference methods for the solution of the equal width ew and regularized long wave rlw equations is reported such an assessment is based on the three invariants of these equations as well as on the magnitude of the errors of the numerical solution and has been performed as a function of the time step and grid spacing two of the methods presented here make use of three point fourth order accurate finite difference formulae for the first and second order spatial derivatives two methods are based on the analytical solution of second order ordinary differential equations which have locally exponential solutions and the fourth technique is a standard finite difference scheme a linear stability analysis of the four methods is presented it is shown that for the ew and rlw equations a compact operator method is more accurate than locally exponential techniques that make use of compact operator approximations the latter are reported to be more accurate than exponential techniques that employ second order accurate approximations and these in turn are more accurate than the standard explicit method

solitary wave solutions for the general kdv equation by adomian decomposition method in recent publications chaos solitons fractals 12 2001 2283 int j appl math 3 4 2000 361 we have dealt with the numerical solutions of the korteweg de vries kdv and modified korteweg de vries mkdv equations we extend this study to a more general nonlinear equation which is the general korteweg de vries gkdv equation in which the previous studies is a special case of it the method applied here is adomian decomposition method which has been developed by george adomian solving frontier problems of physics the decomposition method kluwer academic publishers boston ma 1994 numerical examples are tested to illustrate the pertinent feature of the proposed algorithm

a finite difference scheme for the mrlw and solitary wave interactions the modified regularized long wave mrlw equation is solved numerically using the finite difference method fourier stability analysis of the linearized scheme shows that it is a marginally stable also the local truncation error of the method is investigated three invariants of motion are evaluated to determine the conservation properties of the problem and the numerical scheme leads to accurate and efficient results moreover interaction of two and three solitary waves is shown the development of the maxwellian initial condition into solitary waves is also shown and we show that the number of solitons which are generated from the maxwellian initial condition can be determined numerical results show also that a tail of small amplitude appears after the interactions

numerical schemes for a model for nonlinear dispersive waves abstract a description is given of a number of numerical schemes to solve an evolution equation that arises when modelling the propagation of water waves in a channel the discussion also includes the results of numerical experiments made with each of the schemes it is suggested on the basis of these experiments that one of the schemes may have discrete solitary wave solutions

constructing of exact solutions to the kdv and burgers equations with power law nonlinearity by the extended g g expansion method abstract the extended g g expansion method is introduced to construct more general exact traveling wave solutions to the kdv and burgers equations with any order nonlinear terms the traveling wave solutions are expressed by the hyperbolic functions the trigonometric functions and the rational functions when the parameters take up special values new solitary periodic and complex solutions are also derived from the traveling wave solutions

computations of critical groups and applications to asymptotically linear wave equation and beam equation in this paper by using the morse index theory for strongly indefinite functionals developed in nonlinear anal tma in press we compute precisely the critical groups at the origin and at infinity respectively the abstract theorems are used to study the existence multiplicity of nontrivial periodical solutions for asymptotically wave equation and beam equation with resonance both at infinity and at zero

painleve analysis and lie group symmetries of the regularized long wave equation the painleve formulation is given for the regularized long wave equation which has been used to describe shallow water waves and drift waves in a plasma the lie group symmetries of the equation is then studied and it is shown that the only symmetries are due to the three conserved quantities

mixed galerkin finite element methods for modified regularized long wave equation in this paper mixed galerkin finite methods for modified regularized long wave mrlw equation are studied we discrete in space by finite elements and for the time discretization by extrapolated crank nicolson scheme and explicit linear multistep scheme linear stability analysis based on von neumann theory are performed numerical experiments verify the efficiency and accuracy of the proposed numerical schemes

fully discrete galerkin methods for the korteweg de vries equation abstract fully discrete schemes for the numerical simulation of solutions of the periodic initial value problem for the korteweg de vries equation are introduced implemented and tested of special interest are stable schemes featuring rates of convergence of order higher than two in both the spatial and temporal variable a careful analysis of the relative and absolute efficiency of these schemes is carried out and one of the schemes is applied to demonstrate that solutions of certain generalized korteweg de vries equations apparently may develop singularities in finite time

local momentum preserving algorithms for the grlw equation abstract in this paper four local momentum preserving lmp algorithms for the grlw equation are studied the proposed algorithms which conserve the local momentum conservation in any local time space region are proved to be momentum and mass preserving globally with appropriate boundary conditions two of the algorithms are explicit and the other two are implicit we make nonlinear convergence and stability analysis for the implicit algorithms numerical experiments confirm the long time preservation of the proposed algorithms and verify the theoretical analysis

conservative scheme for a model of nonlinear dispersive waves and its solitary waves induced by boundary motion abstract a conservative difference scheme is given for a model of nonlinear dispersive waves convergence and stability of the scheme are proved by means of this scheme we explore numerically the relationship between the boundary data and the amplitudes and number of solitary waves it produces

numerical implementation for solving the symmetric regularized long wave equation the paper presents a novel finite difference method for the symmetric regularized long wave equation the time discretization is performed by using a four level average difference technique for solving the fluid velocity independently from the density at this stage the numerical solution is easily solved by using the presented method since it does not require an extra effort to deal with a nonlinear term and the density the existence and uniqueness of the numerical solution and the conservation of mass are guaranteed the stability and convergence of the numerical solution with second order accuracy on both space and time are also verified numerical results are carried out to confirm the accuracy of our theoretical results and the efficiency of the scheme to illustrate the effectiveness and the advantage of the proposed method the results at long time behavior are compared with the ones obtained from previously known methods moreover in the computation the present method is applied to the collision of solitons under the effect of variable parameters

solvability of the cauchy problem of nonlinear beam equations in besov spaces abstract in this paper we study solvability of the cauchy problem of the nonlinear beam equation t 2 u 2 u u p with initial data in besov spaces we prove that for any 1 q the cauchy problem of this equation is locally well posed in the besov spaces b 2 q s p r n and b 2 q s r n where s p n 2 4 p 1 and s s p and globally well posed in these spaces if initial data are small moreover we obtain scattering results in b 2 q s p r n

time behaviour of the error when simulating finite band periodic waves the case of the kdv equation this paper is devoted to study the error growth of numerical time integrators for n phase or n band quasi periodic in time solutions of the periodic korteweg de vries equation it is shown that the preservation through numerical time integration of conserved quantities of the periodic problem of the equation may be an element to take into account in the selection of the numerical method we explain why the inclusion of these properties of conservation provides a better error propagation in particular we emphasize how the preservation of invariants makes influence in the simulation of some physical parameters of the waves