A numerical study of the long wave--short wave interaction equations

DOI10.1016/j.matcom.2006.10.016zbMath1130.74053OpenAlexW2082724342MaRDI QIDQ871070

H. A. Erbay, Gulcin M. Muslu, Handan Borluk

Publication date: 15 March 2007

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.matcom.2006.10.016

zbMATH Keywords

solitary wavesrelaxation methodsplit-step methodlong wave--short wave interaction equations

Mathematics Subject Classification ID

Wave scattering in solid mechanics (74J20) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) NLS equations (nonlinear Schrödinger equations) (35Q55) Finite difference methods applied to problems in solid mechanics (74S20)

Related Items (7)

A Novel Approach with Time-Splitting Spectral Technique for the Coupled Schrödinger–Boussinesq Equations Involving Riesz Fractional Derivative ⋮ The time-splitting Fourier spectral method for the coupled Schrödinger-Boussinesq equations ⋮ Numerical simulation of blow-up solutions for the generalized Davey–Stewartson system ⋮ WKB analysis for the three coupled long wave–short wave interaction equations ⋮ Numerical study of blow-up to the purely elliptic generalized Davey-Stewartson system ⋮ Bifurcation and nonsmooth dynamics of solitary waves in the generalized long-short wave equations ⋮ Dynamical behavior of traveling wave solutions of a long waves-short waves resonance model

Cites Work

• Local spectral time splitting method for first- and second-order partial differential equations
• The resonant interaction among long and short waves
• A split-step Fourier method for the complex modified Korteweg-de Vries equation.
• Nonlinear interaction between long and short waves in a generalized elastic solid
• Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation
• A fast spectral algorithm for nonlinear wave equations with linear dispersion
• A General Theory for Interactions Between Short and Long Waves
• Order Estimates in Time of Splitting Methods for the Nonlinear Schrödinger Equation
• A Relaxation Scheme for the Nonlinear Schrödinger Equation
• Numerical study of the Davey-Stewartson system
• A numerical study of the long-wave short-wave resonance for 3D water waves

This page was built for publication: A numerical study of the long wave--short wave interaction equations