Title

Symmetry reductions and new exact invariant solutions of the generalized Burgers equation arising in nonlinear acoustics

Authors

Authors

C. W. Soh

Comments

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Abbreviated Journal Title

Int. J. Eng. Sci.

Keywords

generalized Burgers equation; symmetry classification; lie point; symmetries; potential symmetries; conditional symmetries; symmetry; reduction; CYLINDRICAL N-WAVES; DIFFERENTIAL-EQUATIONS; PROPAGATION; Engineering, Multidisciplinary

Abstract

We perform a complete Lie symmetry classification of the generalized Burgers equation arising in nonlinear acoustics. We obtain seven functional forms of the ray tube area that allow symmetry reductions. We use symmetries to obtain reduced equations and exact solutions when possible. We also investigate the existence of potential symmetries for the generalized Burgers equation. It is found that only the classical Burgers equation admits true potential symmetries. We further obtain all conditional symmetries of the second kind and indicate a possible route for obtaining conditional symmetries of the first kind. The conditional symmetries of the second kind leads to symmetry reductions and exact solutions not obtainable from Lie point symmetries. (C) 2004 Elsevier Ltd. All rights reserved.

Journal Title

International Journal of Engineering Science

Volume

42

Issue/Number

11-12

Publication Date

1-1-2004

Document Type

Article

Language

English

First Page

1169

Last Page

1191

WOS Identifier

WOS:000223041200005

ISSN

0020-7225

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