Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations

DOI

10.2991/jnmp.1999.6.1.6How to use a DOI?

Abstract

In this paper we study symmetry reductions of a class of nonlinear fourth order partial differential equations utt = u + u2 xx + uuxxxx + µuxxtt + uxuxxx + u2 xx, (1) where , , , and µ are arbitrary constants. This equation may be thought of as a fourth order analogue of a generalization of the Camassa-Holm equation, about which there has been considerable recent interest. Further equation (1) is a "Boussinesqtype" equation which arises as a model of vibrations of an anharmonic mass-spring chain and admits both "compacton" and conventional solitons. A catalogue of symmetry reductions for equation (1) is obtained using the classical Lie method and the nonclassical method due to Bluman and Cole. In particular we obtain several reductions using the nonclassical method which are not obtainable through the classical method.

Copyright

© 2006, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Peter A. Clarkson
AU  - Thomas J. Priestley
PY  - 1999
DA  - 1999/02/01
TI  - Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations
JO  - Journal of Nonlinear Mathematical Physics
SP  - 66
EP  - 98
VL  - 6
IS  - 1
SN  - 1776-0852
UR  - https://doi.org/10.2991/jnmp.1999.6.1.6
DO  - 10.2991/jnmp.1999.6.1.6
ID  - Clarkson1999
ER  -