# American Institute of Mathematical Sciences

2015, 2015(special): 151-158. doi: 10.3934/proc.2015.0151

## 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, Spain, Spain, Spain

Received  September 2014 Revised  December 2014 Published  November 2015

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.
Citation: M. S. Bruzón, M. L. Gandarias, J. C. Camacho. Classical and nonclassical symmetries and exact solutions for a generalized Benjamin equation. Conference Publications, 2015, 2015 (special) : 151-158. doi: 10.3934/proc.2015.0151
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