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Study on an extended Boussinesq equation |
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| Authors: | Chen Chun-Li Zhang Jin E Li Yi-Shen |
| Affiliation: | Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China ; SB and SEF, The University of Hong Kong,Pokfulam Road, Hong Kong, China; Department of Mathematics, University of Science and Technology of China, Hefei 230026, China |
| Abstract: | An extended Boussinesq equation that models weakly nonlinear andweakly dispersive waves on a uniform layer of water is studied inthis paper. The results show that the equation is notPainlev'e-integrable in general. Some particular exact travellingwave solutions are obtained by using a function expansion method. Anapproximate solitary wave solution with physical significance isobtained by using a perturbation method. We find that the extendedBoussinesq equation with a depth parameter of $1/sqrt 2$ is able tomatch the Laitone's (1960) second order solitary wave solution ofthe Euler equations. |
| Keywords: | Painlev'e-integrability exact soliton solutions approximate solution |
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