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Classification of bounded travelling wave solutions for the Dullin-Gottwald-Holm equation

Published 3 Jul 2018 in math-ph, math.AP, and math.MP | (1807.01403v1)

Abstract: In this paper we classify all bounded travelling wave solutions for the integrable Dullin-Gottwald-Holm equation. It is shown that it decomposes in two known cases: the Camassa-Holm and the Korteweg-de Vries equation. For the former, the classification is similar to the one presented in [J. Lenells, Travelling wave solutions of the Camassa-Holm equation, J. Diff. Eq., v. 217, 393-430, (2005)], while for the latter it is only possible to obtain smooth solutions.

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