Abstract In this paper, we derive a new exponential wave integrator sine pseudo-spectral (EWI-SP) method for the higher-order Boussinesq equation involving effects of dispersion. The is fully-explicit and it has fourth order accuracy in time spectral space. We rigorously carry out error analysis establish bounds Sobolev spaces. performance EWI-SP illustrated by examining long-time evolution single solitary wave, splitting, head-on collision waves. Numerical experiments confirm theoretical results.

In this article, we propose a Fourier pseudospectral method for solving the generalized improved Boussinesq equation. We prove convergence of semi‐discrete scheme in energy space. For various power nonlinearities, consider three test problems concerning propagation single solitary wave, interaction two waves and solution that blows up finite time. compare our numerical results with those given literature terms accuracy. The comparisons show provides highly accurate results. © 2014 Wiley...

Abstract The existence, uniqueness, and stability of periodic traveling waves for the fractional Benjamin–Bona–Mahony equation is considered. In our approach, we give sufficient conditions to prove a uniqueness result single‐lobe solution obtained by constrained minimization problem. spectral then shown determining that associated linearized operator around wave restricted orthogonal tangent space related momentum mass at has no negative eigenvalues. We propose Petviashvili's method...

In this paper, we study a general class of nonlocal nonlinear coupled wave equations that includes the convolution operation with kernel functions. For appropriate selections functions, system becomes well-known equations, for instance Toda lattice system, improved Boussinesq equations. A numerical scheme is proposed solitary solutions using Pethiashvili method. Using different kernels, validity method has been tested.

The present paper is concerned with the existence of solitary wave solutions Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results waves three different forms are derived. depend on conditions speed respect to parameters They discussed for several families Rosenau equations in literature. analysis illustrated a numerical study generation approximate solitary-wave profiles from procedure based Petviashvili iteration.

Abstract A class of nonlocal nonlinear wave equation arises from the modeling a one dimensional motion in nonlinearly, nonlocally elastic medium. The involves kernel function with nonnegative Fourier transform. We discretize by using spectral method space and we prove convergence semidiscrete scheme. then use fully‐discrete scheme, that couples pseudo‐spectral 4th order Runge‐Kutta time, to observe effect on solutions. To generate solitary solutions numerically, Petviashvili's iteration method.

Blow-up solutions for the generalized Davey–Stewartson system are studied numerically by using a split-step Fourier method. The numerical method has spectral-order accuracy in space and first-order time. To evaluate ability of to detect blow-up, simulations conducted several test problems, results compared with analytical available literature. Good agreement between is observed.

The present paper is concerned with the existence of solitary wave solutions Rosenau-type equations. By using two standard theories, Normal Form Theory and Concentration-Compactness Theory, some results waves three different forms are derived. depend on conditions speed respect to parameters They discussed for several families Rosenau equations in literature. analysis illustrated a numerical study generation approximate solitary-wave profiles from procedure based Petviashvili iteration.

In this paper, we present new results regarding the orbital stability of solitary standing waves for general fourth-order Schr\"odinger equation with mixed dispersion. The existence can be determined both as minimizers a constrained complex functional and by using numerical approach. addition, specific values frequency associated wave, one obtains explicit solutions hyperbolic secant profile. Despite these being functional, they cannot seen smooth curve waves, fact prevents their...

The Klein-Gordon-Boussinesq (KGB) system is proposed in the literature as a model problem to study validity of approximations long wave limit provided by simpler equations such KdV, nonlinear Schr\"{o}dinger or Whitham equations. In this paper, KGB analyzed mathematical three specific points. first one concerns well-posedness initial-value with local existence and uniqueness solution conditions under which global blows up at finite time. second point focused on traveling solutions system....