Classification of bounded travelling wave solutions for the Dullin-Gottwald-Holm equation
Priscila Leal da Silva
TL;DR
This paper classifies all bounded travelling wave solutions of the integrable Dullin-Gottwald-Holm equation, showing it decomposes into cases similar to the Camassa-Holm and Korteweg-de Vries equations, with smooth solutions only for the latter.
Contribution
It provides a complete classification of bounded travelling wave solutions for the Dullin-Gottwald-Holm equation, linking it to known equations and solutions.
Findings
Decomposition into Camassa-Holm and Korteweg-de Vries cases
Classification similar to previous Camassa-Holm solutions
Only smooth solutions for the Korteweg-de Vries case
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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