Abstract:We perform a complete study by using the theory of invariant point transformations and the singularity analysis for the generalized Camassa-Holm equation and the generalized Benjamin-Bono-Mahoney equation.From the Lie theory we find that the two equations are invariant under the same three-dimensional Lie algebra which is the same Lie algebra admitted by the Camassa-Holm equation. We determine the onedimensional optimal system for the admitted Lie symmetries and we perform a complete classification of the simi… Show more
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