Conditionally invariant solutions of the rotating shallow water wave equations

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Abstract

This paper is devoted to the extension of the recently proposed conditional symmetry method to first order nonhomogeneous quasilinear systems which are equivalent to homogeneous systems through a locally invertible point transformation. We perform a systematic analysis of the rank-1 and rank-2 solutions admitted by the shallow water wave equations in (2 + 1) dimensions and construct the corresponding solutions of the rotating shallow water wave equations. These solutions involve in general arbitrary functions depending on Riemann invariants, which allow us to construct new interesting classes of solutions.
Original languageEnglish
Pages (from-to)235205
JournalJournal of Physics A: Mathematical and Theoretical
Volume43
Issue number23
DOIs
Publication statusPublished - 2010

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