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

2018/07/03 by Priscila Leal da Silva, da Silva, Priscila Leal
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1807.01403

openalex publication_date 2018/07/03 · openalex created_date 2022/08/04 · openalex updated_date 2026/07/28

Abstract

In this paper we classify all bounded travelling wave solutions for the\nintegrable Dullin-Gottwald-Holm equation. It is shown that it decomposes in two\nknown cases: the Camassa-Holm and the Korteweg-de Vries equation. For the\nformer, the classification is similar to the one presented in [J. Lenells,\nTravelling wave solutions of the Camassa-Holm equation, J. Diff. Eq., v. 217,\n393-430, (2005)], while for the latter it is only possible to obtain smooth\nsolutions.\n

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