Title

Symmetry Reductions And New Exact Invariant Solutions Of The Generalized Burgers Equation Arising In Nonlinear Acoustics

Keywords

Conditional symmetries; Generalized Burgers equation; Lie point symmetries; Potential symmetries; Symmetry classification; Symmetry reduction

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. © 2004 Elsevier Ltd. All rights reserved.

Publication Date

7-1-2004

Publication Title

International Journal of Engineering Science

Volume

42

Issue

11-12

Number of Pages

1169-1191

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/j.ijengsci.2004.01.004

Socpus ID

3142565185 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/3142565185

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