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.
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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.
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)|
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