Normalized traveling solitary waves for a class of nonlinear half-wave equations. (August 2021) - Zhang, Guoqing; Liang, Chuchu; Zhao, Dun
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.