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September 28, 2025Open Access

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

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Authors

HMHayato MiyazakiOkayama University of ScienceMSMotohiro Sobajima

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Implication

This analysis shows the absence of scattering states for nonlinear Schrödinger equations, indicating key thresholds in nonlinearity.

Key Points

  • No scattering states exist for the considered nonlinear Schrödinger equation in a weighted Sobolev space.
  • The study highlights that the Strauss exponent serves as a crucial threshold for determining scattering solutions.
  • Initial data can include well-behaved functions like compactly supported smooth functions.
  • The method employed involves analyzing a non-oscillatory term with a power lower than the Strauss exponent.

Cite This Study

Miyazaki et al. (2025) studied this question.

synapsesocial.com/papers/68d90a0f41e1c178a14f6b6ahttps://doi.org/10.48550/arxiv.2503.07983
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Also Consider

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