Travelling wave solutions for some two-component shallow water models

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:261

Article

Dutykh, Denys¹  Ionescu-Kruse, Delia² 

[1] Univ Savoie Mt Blanc, UMR CNRS 5127, LAMA, Campus Sci, F-73376 Le Bourget Du Lac, France

[2] Romanian Acad, Simion Stoilow Inst Math, Res Unit 6, POB 1-764, RO-014700 Bucharest, Romania

关键词: Travelling waves;    Cnoidal waves;    Solitary waves;    Green-Naghdi model;    Camassa-Holm equations;    Serre equations;    Phase-plane analysis;   

DOI  :  10.1016/j.jde.2016.03.035

来源: Elsevier

【 摘 要 】

In the present study we perform a unified analysis of travelling wave solutions to three different two component systems which appear in shallow water theory. Namely, we analyze the celebrated Green Naghdi equations, the integrable two-component Camassa-Holm equations and a new two-component system of Green-Naghdi type. In particular, we are interested in solitary and cnoidal-type solutions, as two most important classes of travelling waves that we encounter in applications. We provide a complete phase-plane analysis of all possible travelling wave solutions which may arise in these models. In particular, we show the existence of new type of solutions. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free