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Symmetries and exact solutions for a 2 + 1-dimensional shallow water wave equation

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  • Mansfield, Elizabeth L.
  • Clarkson, Peter A.

Abstract

Classical and nonclassical reductions of a 2 + 1-dimensional shallow water wave equation are classified. Using these reductions, we derive some exact solutions, including solutions expressed as the nonlinear superposition of solutions of a generalised variable-coefficient Korteweg-de Vries equation. Many of the reductions obtained involve arbitrary functions and so the associated families of solutions have a rich variety of qualitative behaviours. This suggests that solving the initial value problem for the 2 + 1-dimensional shallow water equation under discussion could pose some fundamental difficulties.

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  • Mansfield, Elizabeth L. & Clarkson, Peter A., 1997. "Symmetries and exact solutions for a 2 + 1-dimensional shallow water wave equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(1), pages 39-55.
    • Handle: RePEc:eee:matcom:v:43:y:1997:i:1:p:39-55
    DOI: 10.1016/S0378-4754(96)00054-7
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    Cited by:

    1. Mrutyunjaya Sahoo & Snehashish Chakraverty, 2022. "Sawi Transform Based Homotopy Perturbation Method for Solving Shallow Water Wave Equations in Fuzzy Environment," Mathematics, MDPI, vol. 10(16), pages 1-24, August.

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