Potential symmetries of the nonlinear wave equation [iopmath latex="$ u_{tt}=(uu_x)_x$"] u_tt = (uu_x)_x [/iopmath] and related exact and approximate solutions

Author: Burde G.I.

Source: Journal of Physics A: Mathematical and General, Volume 34, Number 26, 2001 , pp. 5355-5371(17)

Publisher: IOP Publishing

Abstract:

This paper explores potential symmetries of the nonlinear wave equation [iopmath latex="$u_{tt}=(uu_x)_x$"] u_tt = (uu_x)_x [/iopmath] , as well as related new similarity reductions and exact solutions of this equation. New approximate solutions of the perturbed nonlinear equations stemming from the exact solutions of the equation are obtained by applying a new approach to the use of the Lie group technique for differential equations dependent on a small parameter. In addition, some nonlinear wave equations exactly reducible to the equation [iopmath latex="$u_{tt}=(uu_x)_x$"] u_tt = (uu_x)_x [/iopmath] are constructed using this approach.

Language: English

Document Type: Miscellaneous

Publication date: 2001-01-01

• In this: publication
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• In this Subject: Mathematics and Statistics ,  Physics (General)
• By this author: Burde G.I.

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