Painleve property and exact solutions for a nonlinear wave equation with generalized power-law nonlinearities

    Authors

    M. Russo; R. A. Van Gorder;S. R. Choudhury

    Comments

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    Abbreviated Journal Title

    Commun. Nonlinear Sci. Numer. Simul.

    Keywords

    Painleve analysis; Nonlinear hyperbolic PDE; Power-law nonlinearity; Exact solutions; PARTIAL-DIFFERENTIAL-EQUATIONS; SOLITON-SOLUTIONS; Mathematics, Applied; Mathematics, Interdisciplinary Applications; Mechanics; Physics, Fluids & Plasmas; Physics, Mathematical

    Abstract

    By employing a variety of techniques, we investigate several classes of solutions of a family of nonlinear partial differential equations (NLPDEs) with generalized nonlinearities, special cases of which include the Klein-Gordon equation, the Landau-Ginzburg-Higgs equation, the phi(4) and phi(6) equations, the Rayleigh wave equation. The Painleve property for our class of equations is studied first, showing that there are integrable families of such equations satisfying the strong Painleve property (under a traveling wave assumption). From the truncated Laurent expansions, we introduce the auto-Backlund transformation for the two families shown to admit the strong Painleve property. A multi-parameter family of exact solutions is then constructed from these auto-Backlund transformations for each of the cases, leading to travelling wave solutions. From here, assuming only travelling wave solutions, we then discuss more general methods of obtaining travelling wave solutions for those cases which do not satisfy the strong Painleve property. Such solutions constitute rare exact solutions to a complicated nonlinear partial differential equation. (c) 2012 Elsevier B.V. All rights reserved.

    Journal Title

    Communications in Nonlinear Science and Numerical Simulation

    Volume

    18

    Issue/Number

    7

    Publication Date

    1-1-2013

    Document Type

    Article

    Language

    English

    First Page

    1623

    Last Page

    1634

    WOS Identifier

    WOS:000314870400007

    ISSN

    1007-5704

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