Clarkson, P.A. and Priestley, T.J.
(1998)
*Shallow water wave systems.*
Studies in Applied Mathematics, 101
(4).
pp. 389-432.
ISSN 0022-2526.
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Official URL http://dx.doi.org/10.1111/1467-9590.00099 |

## Abstract

In this article we study various systems that represent the shallow water wave equation upsilon(xxt) + alpha upsilon upsilon(t) - beta upsilon(x)partial derivative(x)(-1) (upsilon(t)) -upsilon(t) - upsilon(x) = 0, (1) where (partial derivative(x)(-1)f)(x) = integral(x)(infinity)f(y) dy, and alpha and beta are arbitrary, nonzero, constants, The classical method of Lie, the nonclassical method of Bluman and Cole [J. Math. Mech. 18:1025 (1969)], and the direct method of Clarkson and Kruskal [J. Math. Phys. 30:2201 (1989)] are each applied to these systems to obtain their symmetry reductions. It is shown that for both the nonclassical and direct methods unusual phenomena can occur, which leads us to question the relationship between these methods for systems of equations. In particular an example is exhibited in which the direct method obtains a reduction that the nonclassical method does not.

Item Type: | Article |
---|---|

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Applied Mathematics |

Depositing User: | I. Ghose |

Date Deposited: | 04 Apr 2009 08:10 |

Last Modified: | 04 Apr 2009 08:10 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/17649 (The current URI for this page, for reference purposes) |

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