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Similarity Reductions For A Generalized Variable-Coefficient Kadomtsev–Petviashvili Equation With Symbolic Computation

Author

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  • BO TIAN

    (Department of Applied Mathematics, Beijing University of Aeronautics and Astronautics, Engineering Research Institute, Beijing University, Beijing 100083, China)

Abstract

We use computerized symbolic computation to study the similarity reductions of a generalized Kadomtsev–Petviashvili (KP) equation, with its space- and time-dependent coefficients arising in plasma physics and fluid mechanics. We obtain a couple of reductions involving those coefficient functions, one of which is to the fourth Painlevé equation, while the other is to one of the second Painlevé equation, the first Painlevé equation or a Weierstrass elliptic function equation. Our results agree with the Painlevé Conjecture. The cylindrical KP equation is presented as an example, which describes nonlinear cylindrical water waves in shallow water with a weak azimuthal dependence.

Suggested Citation

  • Bo Tian, 1999. "Similarity Reductions For A Generalized Variable-Coefficient Kadomtsev–Petviashvili Equation With Symbolic Computation," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 10(06), pages 1089-1097.
    • Handle: RePEc:wsi:ijmpcx:v:10:y:1999:i:06:n:s0129183199000899
    DOI: 10.1142/S0129183199000899
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