Decay property of solutions near the traveling wave solutions for the second-order Camassa–Holm equation. (June 2019)

• Record Type: Journal Article
• Authors: Ding, Danping; Wang, Kai
• Is Part Of: Nonlinear analysis. Volume 183(2019)
• Page Start: 230
• Page End: 258
• Publication Date: 2019-06
• Subjects: 35B30 -- 35B35 -- 35G20 -- 35G25 -- 47A50; Second-order Camassa–Holm equation -- Decay -- Traveling wave solution -- Pseudo-conformal transformation; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2019.01.018
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper studies the decay properties of solutions around the traveling wave solutions for Cauchy problem of the second-order Camassa–Holm equation. Applying the extended pseudo-conformal transformation methods, appearing the relevant works on the generalized Korteweg–de Vries equation (KdV) and nonlinear Schrödinger equation (NLS) from Martel and Merle, the solution is controlled by the decaying function with exponential speed, corresponding to the initial data and its second derivative with exponential decay.