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- Title
Invariant and Partially Invariant Solutions of the Green-Naghdi Equations.
- Authors
Bagderina, Yu. Yu.; Chupakhin, A. P.
- 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.
- Subjects
PAINLEVE equations; NONLINEAR differential equations; NONLINEAR theories; ELLIPTIC functions; TRANSCENDENTAL functions; SPECIAL functions
- Publication
Journal of Applied Mechanics & Technical Physics, 2005, Vol 46, Issue 6, p791
- ISSN
0021-8944
- Publication type
Article
- DOI
10.1007/s10808-005-0136-z