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arXiv · 2503.07983

Threshold for the existence of scattering states for nonlinear Schr\"odinger equations without gauge invariance

Hayato Miyazaki·Motohiro Sobajima
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Abstract

This paper is concerned with a threshold phenomenon for the existence of scattering states for nonlinear Schr\"odinger 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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Hayato Miyazaki, Motohiro Sobajima. 2025-03-11. Threshold for the existence of scattering states for nonlinear Schr\"odinger equations without gauge invariance. https://doi.org/10.1090/proc%2F17398

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