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Licensed Unlicensed Requires Authentication Published by De Gruyter August 15, 2017

On the Shallow Water Equations

  • Mahmoud A.E. Abdelrahman EMAIL logo


We studied the shallow water equations of nonlinear conservation laws. First we studied the parametrisation of nonlinear elementary waves and hence we present the solution to the Riemann problem. We also prove the uniqueness of the Riemann solution. The Riemann invariants are formulated. Moreover we give an interesting application of the Riemann invariants. We present the shallow water system in a diagonal form, which admits the existence of a global smooth solution for these equations. The other application is to introduce new conservation laws for the shallow water equations.

AMS subject classifications: 35L45; 35L60; 35L65; 35L67


The author wants to express deepest gratefulness to the editor and reviewers for valuable comments and suggestions.


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Received: 2017-4-28
Accepted: 2017-7-17
Published Online: 2017-8-15
Published in Print: 2017-8-28

©2017 Walter de Gruyter GmbH, Berlin/Boston

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