Study on an extended Boussinesq equation

• 来源期刊: 中国物理（英文版）
• 关键词: Painlevé-integrability exact soliton solutions approximate solution
• 年，卷（期）: 2007,（8）
• 页码范围: 2167-2179
• 页数: 13页
• 语种: 英文

摘要

An extended Boussinesq equation that models weakly nonlinear and weakly dispersive waves on a uniform layer of water is studied in this paper. The results show that the equation is not Painlevé-integrable in general. Some particular exact travelling wave solutions are obtained by using a function expansion method. An approximate solitary wave solution with physical significance is obtained by using a perturbation method. We find that the extended Boussinesq equation with a depth parameter of 1/√2 is able to match the Laitone's (1960) second order solitary wave solution of the Euler equations.