Chen Chun-Li(陈春丽)a)†, Zhang Jin E(张近)b), and Li Yi-Shen(李翊神)c)
a Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China ; b SB and SEF, The University of Hong Kong,Pokfulam Road, Hong Kong, China; c Department of Mathematics, University of Science and Technology of China, Hefei 230026, China
Abstract 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 $1/\sqrt 2$ is able to match the Laitone's (1960) second order solitary wave solution of the Euler equations.
Received: 11 October 2006
Revised: 23 February 2007
Accepted manuscript online:
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