Abstract
All invariant and partially invariant solutions of the Green-Naghdi equations are obtained that describe the second approximation of shallow water theory. It is proved that all nontrivial invariant solutions belong to one of the following types: Galilean-invariant, stationary, and self-similar solutions. The Galilean-invariant solutions are described by the solutions of the second Painleve equation, the stationary solutions by elliptic functions, and the self-similar solutions by the solutions of the system of ordinary differential equations of the fourth order. It is shown that all partially invariant solutions reduce to invariant solutions.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 26–35, November–December, 2005.
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Bagderina, Y.Y., Chupakhin, A.P. Invariant and Partially Invariant Solutions of the Green-Naghdi Equations. J Appl Mech Tech Phys 46, 791–799 (2005). https://doi.org/10.1007/s10808-005-0136-z
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DOI: https://doi.org/10.1007/s10808-005-0136-z