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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