Classical and nonclassical symmetries and exact solutions for a generalized Benjamin equation

M. S.  Bruzón; M. L.  Gandarias; J. C.  Camacho

doi:10.3934/proc.2015.0151

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2015, Volume 2015: 151-158. Doi: 10.3934/proc.2015.0151 open access

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Classical and nonclassical symmetries and exact solutions for a generalized Benjamin equation

1.
Departamento de Matemáticas, Universidad de Cádiz, PO.BOX 40, 11510 Puerto Real, Cádiz

Received: August 31, 2014

Revised: November 30, 2014

Published: October 2015

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Abstract

We apply the Lie-group formalism to deduce symmetries of a generalized Benjamin equation. We make an analysis of the symmetry reductions of the equation. In order to obtain travelling wave solutions we apply an indirect F-function method. We obtained in an unified way simultaneously many periodic wave solutions expressed by various single and combined nondegenerative Jacobi elliptic function solutions and their degenerative solutions. We compare these solutions with the solutions derived by other authors by using different methods and we observe that we have obtained new solutions for this equation.

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Mathematics Subject Classification: Primary: 35Q35; Secondary: 76M60.

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