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(2+1)-dimensional Broer–Kaup system of shallow water waves and similarity solutions with symbolic computation

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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.

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Authors and Affiliations

  1. School of Science, Beijing University of Posts and Telecommunications, P. O. Box 122, Beijing, 100876, China

    Bo Tian & He Li

  2. State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing, 100083, China

    Bo Tian & Yi-Tian Gao

  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

    Yi-Tian Gao

Authors
  1. Bo Tian
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  2. He Li
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  3. Yi-Tian Gao
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Correspondence to Yi-Tian Gao.

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Received: February 26, 2003; revised: August 11, 2003

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Tian, B., Li, H. & Gao, YT. (2+1)-dimensional Broer–Kaup system of shallow water waves and similarity solutions with symbolic computation. Z. angew. Math. Phys. 56, 783–790 (2005). https://doi.org/10.1007/s00033-005-3021-y

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  • DOI: https://doi.org/10.1007/s00033-005-3021-y

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