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Exact traveling wave solutions and $$L^{1}$$ L 1 stability for the shallow water wave model of moderate amplitude

Exact traveling wave solutions and $$L^{1}$$ L 1 stability for the shallow water wave... In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in $$L^{1}(R)$$ L 1 ( R ) space for the Cauchy problem of the equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Analysis and Mathematical Physics Springer Journals

Exact traveling wave solutions and $$L^{1}$$ L 1 stability for the shallow water wave model of moderate amplitude

Analysis and Mathematical Physics , Volume 7 (3) – Jul 21, 2016

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Publisher
Springer Journals
Copyright
Copyright © 2016 by Springer International Publishing
Subject
Mathematics; Analysis; Mathematical Methods in Physics
ISSN
1664-2368
eISSN
1664-235X
DOI
10.1007/s13324-016-0139-3
Publisher site
See Article on Publisher Site

Abstract

In this paper, we developed, for the first time, the exact expressions of several periodic travelling wave solutions and a solitary wave solution for a shallow water wave model of moderate amplitude. Then, we present the existence theorem of the global weak solutions. Finally, we prove the stability of solution in $$L^{1}(R)$$ L 1 ( R ) space for the Cauchy problem of the equation.

Journal

Analysis and Mathematical PhysicsSpringer Journals

Published: Jul 21, 2016

References