Startseite Lie Symmetries, One-Dimensional Optimal System and Group Invariant Solutions for the Ripa System
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Lie Symmetries, One-Dimensional Optimal System and Group Invariant Solutions for the Ripa System

  • Pabitra Kumar Pradhan und Manoj Pandey EMAIL logo
Veröffentlicht/Copyright: 16. Juli 2019
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Abstract

A complete symmetry group classification for the system of shallow water equations with the horizontal temperature gradient, also known as Ripa system, is presented. A rigorous and systematic procedure based on the general invariants of the adjoint representation is used to construct the one-dimensional optimal system of the Lie algebra. The complete inequivalence class of the group invariant solutions are obtained by using the one-dimensional optimal system. One such solution of the Ripa system is used to study the evolutionary behaviour of the discontinuity wave.

MSC 2010: 70G65; 35L40

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Received: 2018-10-13
Accepted: 2019-06-25
Published Online: 2019-07-16
Published in Print: 2019-10-25

© 2019 Walter de Gruyter GmbH, Berlin/Boston

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