The orbital stability of the periodic traveling wave solutions to the defocusing complex modified Korteweg–de Vries equation. (February 2023)

• Record Type: Journal Article
• Authors: Sun, Wen-Rong
• Is Part Of: Nonlinear analysis. Volume 227(2023)
• Publication Date: 2023-02
• Subjects: 37K45 -- 35Q55 -- 33E05; Stability -- Defocusing cmKdV equation -- Elliptic solution -- Subharmonic perturbations -- Integrability; 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.2022.113155
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: The stability of the elliptic solutions to the defocusing complex modified Korteweg–de Vries (cmKdV) equation is studied. Using the integrability of the defocusing cmKdV equation, we prove the spectral stability of the elliptic solutions. We show that one special linear combination of the first seven conserved quantities produces a Lyapunov functional, which implies that the elliptic solutions are orbitally stable with respect to the subharmonic perturbations.