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

Mansfield, E.L. and Clarkson, P.A. (1997) Symmetries and exact solutions for a 2+1-dimensional shallow water wave equation. Mathematics and Computers in Simulation, 43 (1). pp. 39-55. ISSN 0378-4754. (The full text of this publication is not available from this repository)

The full text of this publication is not available from this repository. (Contact us about this Publication)
Official URL
http://dx.doi.org/10.1016/S0378-4754(96)00054-7

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. The nonlinear overdetermined systems of partial differential equations whose solutions yield the reductions were analysed and solved using the MAPLE package diffgrob2, which we describe briefly.

Item Type: Article
Subjects: Q Science
Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer science
Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Divisions: Faculties > Science Technology and Medical Studies > School of Computing
Depositing User: M.A. Ziai
Date Deposited: 19 Apr 2009 21:52
Last Modified: 19 Apr 2009 21:52
Resource URI: http://kar.kent.ac.uk/id/eprint/18173 (The current URI for this page, for reference purposes)
  • Depositors only (login required):