Exact solitary-wave solutions and periodic wave solutions for generalized modified Boussinesq equation and the effect of wave velocity on wave shape

DOI10.1007/S10255-007-7048-ZzbMath1151.35416OpenAlexW2008202310MaRDI QIDQ950678

Weizhong Tian, Lu Zhang, Shaowei Li, Wei-Guo Zhang

Publication date: 27 October 2008

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10255-007-7048-z

zbMATH Keywords

periodic wave solutiongeneralized modified Boussinesq equationexact solitary-wave solution

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) KdV equations (Korteweg-de Vries equations) (35Q53) Periodic solutions to PDEs (35B10) Soliton equations (35Q51)

Cites Work

• Unnamed Item
• A note on the non-existence of global solutions of initial boundary value problems for the Boussinesq equation \(u_{tt}=3u_{xxxx}+u_{xx}- 12(u^ 2)_{xx}\)
• Global existence of small solutions for a generalized Boussinesq equation
• Methods of judging shape of solitary wave and solution formulae for some evolution equations with nonlinear terms of high order.
• The Painlevé property, a modified Boussinesq equation and a modified Kadomtsev-Petviashvili equation
• Blow-up of solutions for improved Boussinesq type equation
• Nonlinear variants of the improved Boussinesq equation with compact and noncompact struc\-tures
• New similarity reductions of the Boussinesq equation
• Stability of solitary waves in shallow water

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