Doubly periodic solutions of the coupled scalar field equations
type: Item
instance of: scholarly article
title: Doubly periodic solutions of the coupled scalar field equations
zbMATH Open document ID: 1074.34004
author: Chun-Ping Liu
published in: Chaos, Solitons and Fractals
publication date: 2005-04-21T00:00:00Z
review text: Seventeen kinds of doubly periodic solutions of the coupled Schrödinger-Boussinesq equations \[ \frac{d^2\psi}{d^2\xi}= \alpha_1\psi+\alpha_2\psi\phi,\qquad \frac{d^2\phi}{d^2\xi}= \beta_1\phi+\beta_2\phi^2+\beta_3\psi^2, \] are presented in closed form. The author introduces an auxiliary ordinary differential equation and uses its Jacobi elliptic function solution to construct doubly periodic solutions of the coupled equations. When the module \(m\to 1\), then these solutions degenerate to exact solitary wave solutions of the coupled equations.
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 2160106
zbMATH Keywords: Schrödinger-Boussinesq equation
zbMATH Keywords: Jacobi elliptic function
zbMATH Keywords: exact solitary wave solution
reviewed by: Valeriy Yumaguzhin
MaRDI profile type: Publication
full work available at URL: j.chaos.2004.03.022
OpenAlex ID: W1977487796
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DOI: 10.1016/J.CHAOS.2004.03.022
description: scientific article; zbMATH DE number 2160106