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

    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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