Lie symmetries and invariant solutions of the shallow-water equation
We investigate the Lie symmetries and similarity reductions of the new completely integrable dispersive shallow water equation, through classical and non-classical methods. We compare the similarity reduction thus obtained with the similarity reduction obtained by the direct method. The resultant ordinary differential equation satisfies the Painlevé property and the ARS conjecture. We also point out how the similarity reduction of the present integrable system differs from that of the non-integrable, but closely related, Benjamin-Bono-Mahoney equation.
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