Blow-up solution near the traveling waves for the second-order Camassa–Holm equation. (April 2021)

• Record Type: Journal Article
• Authors: Ding, Danping; Wang, Kai
• Is Part Of: Nonlinear analysis. Volume 58(2021)
• Publication Date: 2021-04
• Subjects: 35B35 -- 35B44 -- 35G25 -- 47A50; Second-order Camassa–Holm equation -- Blow-up -- Traveling wave -- Pseudo-conformal transformation; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2020.103209
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: This paper studies the blow-up solution and its blow-up rate near the traveling waves of the second-order Camassa–Holm equation. The sufficient condition for the existence of blow-up solution is obtained by a rather ingenious method. Applying the extended pseudo-conformal transformation, an equivalent proposition of the solution breaking in finite time near the traveling waves is constructed. The relation is established between the blow-up time and rate of the solution and the residual's. Highlights: The sufficient condition for the existence of blow-up solution. Extended pseudo-conformal transformation. An equivalent proposition of the solution breaking in finite time. The relation between the blow-up time and rate of the solution and residual's.