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

Elizabeth L. Mansfield and Peter A. Clarkson

Mathematics and Computers in Simulation (MATCOM), 1997, vol. 43, issue 1, 39-55

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.

Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:43:y:1997:i:1:p:39-55

DOI: 10.1016/S0378-4754(96)00054-7

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