Volume 6, Issue 1, February 1999, Pages 66 - 98
Symmetries of a Class of Nonlinear Fourth Order Partial Differential Equations
Peter A. CLARKSON, Thomas J. PRIESTLEY
Peter A. CLARKSON
Available Online 1 February 1999.
- https://doi.org/10.2991/jnmp.19184.108.40.206How to use a DOI?
- 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.
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Cite this article
TY - JOUR AU - Peter A. CLARKSON AU - Thomas J. PRIESTLEY PY - 1999 DA - 1999/02 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.19220.127.116.11 DO - https://doi.org/10.2991/jnmp.1918.104.22.168 ID - CLARKSON1999 ER -