Title
Painleve property and exact solutions for a nonlinear wave equation with generalized power-law nonlinearities
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
ISSN
1007-5704
Recommended Citation
"Painleve property and exact solutions for a nonlinear wave equation with generalized power-law nonlinearities" (2013). Faculty Bibliography 2010s. 4628.
https://stars.library.ucf.edu/facultybib2010/4628
Comments
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