Coexistence of the solitary and periodic waves in convecting shallow water fluid. (June 2020)

• Record Type: Journal Article
• Authors: Sun, Xianbo; Huang, Wentao; Cai, Junning
• Is Part Of: Nonlinear analysis. Volume 53(2020)
• Publication Date: 2020-06
• Subjects: Periodic traveling wave -- Solitary wave -- Coexistence; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2019.103067
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: The existence of a solitary wave for the shallow water model in convecting circumstance was established in previous works. It is still unknown that whether there exist periodic waves. In this paper, we prove that the models possess periodic waves with a fixed range of wave speed. The amplitude and wave speed are explicitly given. Moreover, the coexistence of the solitary wave and one periodic wave is established.