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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2005, Volume 46, Issue 6, Pages 26–35
(Mi pmtf2316)
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This article is cited in 8 scientific papers (total in 8 papers)
Invariant and partially invariant solutions of the Green–Naghdi equations
Yu. Yu. Bagderinaa, A. P. Chupakhinb a Institute of Mathematics, Ural Scientific Center, Russian Academy of Sciences, Ufa, 450077, Russia
b Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia
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.
Keywords:
Green–Naghdi equations, invariant and partially invariant solutions, Painleve equation.
Received: 27.01.2005
Citation:
Yu. Yu. Bagderina, A. P. Chupakhin, “Invariant and partially invariant solutions of the Green–Naghdi equations”, Prikl. Mekh. Tekh. Fiz., 46:6 (2005), 26–35; J. Appl. Mech. Tech. Phys., 46:6 (2005), 791–799
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https://www.mathnet.ru/eng/pmtf2316 https://www.mathnet.ru/eng/pmtf/v46/i6/p26
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