Title
Symmetry reductions and new exact invariant solutions of the generalized Burgers equation arising in nonlinear acoustics
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
ISSN
0020-7225
Recommended Citation
"Symmetry reductions and new exact invariant solutions of the generalized Burgers equation arising in nonlinear acoustics" (2004). Faculty Bibliography 2000s. 4812.
https://stars.library.ucf.edu/facultybib2000/4812
Comments
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