Potential symmetries of the nonlinear wave equation utt = (uux)x and related exact and approximate solutions

Georgy I. Burde

doi:10.1088/0305-4470/34/26/306

Potential symmetries of the nonlinear wave equation u_tt = (uu_x)_x and related exact and approximate solutions

Georgy I. Burde

Research output: Contribution to journal › Article › peer-review

16 Scopus citations

Abstract

This paper explores potential symmetries of the nonlinear wave equation u_tt = (uu_x)_x, 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 u_tt = (uu_x)_x are constructed using this approach.

Original language	English
Pages (from-to)	5355-5371
Number of pages	17
Journal	Journal of Physics A: Mathematical and General
Volume	34
Issue number	26
DOIs	https://doi.org/10.1088/0305-4470/34/26/306
State	Published - 6 Jul 2001

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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abstract = "This paper explores potential symmetries of the nonlinear wave equation utt = (uux)x, 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 utt = (uux)x are constructed using this approach.",

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Potential symmetries of the nonlinear wave equation u_tt = (uu_x)_x and related exact and approximate solutions

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