Lamé function and multi-order exact solutions to nonlinear evolution equations
type: Item
instance of: scholarly article
title: Lamé function and multi-order exact solutions to nonlinear evolution equations
zbMATH Open document ID: 1053.35034
DOI: 10.1016/S0960-0779(03)00208-X
author: Shi-Kuo Liu
author: Zuntao Fu
author: Shi-Da Liu
author: Zhanggui Wang
published in: Chaos, Solitons and Fractals
publication date: 2004-07-01T00:00:00Z
review text: The Lamé equation and Lamé functions are applied to solve nonlinear evolution equations. When the perturbation method and two kinds of Lamé functions \(L_3(x)\) and \(L_2(x)\) are considered, then the multi-order solutions are obtained for these nonlinear evolution equations. The results obtained in this paper are very useful for nonlinear instability analysis of nonlinear coherent structures.
Mathematics Subject Classification ID: 35C05
Mathematics Subject Classification ID: 33E10
zbMATH DE Number: 2077274
zbMATH Keywords: Lamé equation
zbMATH Keywords: nonlinear instability
zbMATH Keywords: coherent structures
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
cites work: Solitary wave solutions for variant Boussinesq equations
cites work: Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics
cites work: Exact solutions of nonlinear equations
cites work: Travelling solitary wave solutions to a compound KdV-Burgers equation.
cites work: Exact solutions of nonlinear PDE, nonlinear transformation and reduction of nonlinear PDE to a quadrature
cites work: Extended tanh-function method and its applications to nonlinear equations
cites work: Exact N-soliton solutions of the wave equation of long waves in shallow-water and in nonlinear lattices
cites work: A simple fast method in finding particular solutions of some nonlinear PDE
cites work: A simple transformation for nonlinear waves.
cites work: Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations
cites work: New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations
cites work: Periodical solution to the nonlinear dissipative equation for surface waves in a convecting liquid layer
cites work: Exact periodic solutions of the complex Ginzburg–Landau equation
cites work: Some general periodic solutions to coupled nonlinear Schrödinger equations.
cites work: Q4040545
cites work: Perturbation methods and non-linear hyperbolic waves
description: scientific article; zbMATH DE number 2077274