An Exponential Wave Integrator Pseudospectral Method for the Symmetric Regularized-Long-Wave Equation

Abstract

International audienc

Coupled and decoupled high‐order accurate dissipative finite difference schemes for the dissipative generalized symmetric regularized long wave equations

“…Suppose that u 0 , u 1 , … , u n and 𝜌 0 , 𝜌 1 , … , 𝜌 n satisfy the difference scheme ( 18)-( 21), then we prove that there exist u n+1 and 𝜌 n+1 satisfying Equations ( 18)- (21). For a fixed n, we rewrite Equation (18) and Equation (19) in the term of…”

“…Existence and uniqueness of solutions, existence of global attractors, stability and instability of solitary waves and exact traveling wave solution were studied in References [5][6][7][8]. The well-known numerical methods include the finite difference method [3,[9][10][11][12][13][14][15], the spectral and pseudo spectral methods [16][17][18][19][20][21], the finite element method [22][23][24] and other methods [25,26].…”

Error analysis of an explicit symmetric fourth-order exponential wave integrator Fourier pseudo-spectral method for the Klein-Gordon-Schrödinger equation

“…By working with the two-level scheme in the correct energy space, the rigorous finite time error estimates of the proposed scheme were established without any CFL-type conditions. In [43], Zhao also investigated an exponential wave integrator Fourier pseudo-spectral method for solving the symmetric regularized-long-wave equation. Recently, exponential wave integrator (EWI) pseudo-spectral method has been applied to solve the "good" boussinesq equation [29] and the extended Fisher-Kolmogorov equation [25].…”

Influence of Nonlinear Terms on Orbital Stability of Solitary Wave Solutions to the Generalized Symmetric Regularized-Long-Wave Equation

“…Recent years, many researchers have studied the solitary wave solutions of Eq. ( 1) by various methods [5][6][7][8], such as exp(− ( ) ) extend method [5], tanh function extend method [6], analytical method [7] and exponential wave integrator pseudospectral method [8]. For the stability [9], studied the local and global well posedness problems of solutions to Eq.…”