(2+1)-dimensional Broer–Kaup system of shallow water waves and similarity solutions with symbolic computation |
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| Authors: | Bo Tian He Li Yi-Tian Gao |
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| Institution: | (1) School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing, 100876, China;(2) State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China;(3) Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China |
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| Abstract: | The Broer–Kaup system is among the important integrable models for the shallow water waves. For a (2+1)-dimensional Broer–Kaup system and with symbolic computation, we present some similarity solutions, which are expressible in terms of the Jacobian elliptic functions and second Painlevé transcendent. Our results are in agreement with the Painlevé conjecture.Received: February 26, 2003; revised: August 11, 2003 |
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| Keywords: | 35Q58 76B15 76M99 68W30 |
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