Traveling solutions and evolution properties of the higher order Camassa–Holm equation. (March 2017)

• Record Type: Journal Article
• Authors: Ding, Danping
• Is Part Of: Nonlinear analysis. Volume 152(2017)
• Page Start: 1
• Page End: 11
• Publication Date: 2017-03
• Subjects: 35Bxx -- 35C07 -- 35G25; High-order Camassa–Holm equation -- Traveling solution -- Evolution procedure; 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.2016.12.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper investigates general mild traveling solutions and the stationary solution of the higher-order Camassa–Holm equation. By argument of regularity and conservation, we construct admitted traveling solutions of the second order and the third order Camassa–Holm equations. Furthermore, evolution procedure and evolution properties of a traveling solution are discussed; the discussion reveals the periodic behavior of the traveling solution curve itself and its curvature. These investigations are valuable to understand forming and evolution of a pattern.