Normalized traveling solitary waves for a class of nonlinear half-wave equations. (August 2021)

• Record Type: Journal Article
• Authors: Zhang, Guoqing; Liang, Chuchu; Zhao, Dun
• Is Part Of: Nonlinear analysis. Volume 209(2021)
• Publication Date: 2021-08
• Subjects: 35A15 -- 35J50; Half-wave equation -- Normalized traveling solitary waves -- Minimax approach -- L2-supercritical; 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.2021.112344
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we prove the non-existence and existence of normalized traveling solitary waves for a class of half-wave equations with nonlinear term in the L 2 -supercritical regime. Our results are based on Riesz transforms, minimax approach and Concentration–compactness Lemma. In addition, we also obtain the Cauchy problem of the focusing half-wave equations does not have small data scattering.