Threshold for the existence of scattering states for nonlinear Schrödinger equations without gauge invariance

2025/03/11 by Miyazaki, Hayato, Sobajima, Motohiro
#35P25 #35Q55 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2503.07983

Abstract

This paper is concerned with a threshold phenomenon for the existence of scattering states for nonlinear Schrödinger equations. The nonlinearity includes a non-oscillatory term of the order lower than the Strauss exponent. We show that no scattering states exist for the equation in a weighted Sobolev space. It is emphasized that our method admits initial data with good properties, such as compactly supported smooth functions. The result indicates that the Strauss exponent acts as a threshold for the power of the nonlinearity that determines whether solutions scatter or not in the weighted space.

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