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Study on an extended Boussinesq equation |
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| Authors: | Chen Chun-Li Zhang Jin E and 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 and weakly dispersive waves on a uniform layer of water is studied in this paper. The results show that the equation is not Painlev\'e-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. |
| Keywords: | Painlev\'e-integrability exact soliton solutions approximate solution |
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