PreprintCC BY 4.0arXiv
Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance
Abstract
We consider the asymptotic behavior of solutions to inhomogeneous nonlinear Schrödinger equations with non-gauge-invariant nonlinearities. The spatial coefficient in the nonlinear term may have different orders of singularity at the origin and decay at infinity. Under a coercivity condition involving the coefficient and the nonlinearity, we show that no scattering states exist for the equation below a Strauss-type threshold determined by the decay at infinity. Our class includes nonlinearities with a dominant non-oscillatory component. We also prove a complementary small-data scattering result above this threshold, using non-admissible Strichartz estimates in Lorentz spaces adapted to the singular coefficient.
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BibTeX
@misc{grira2026threshold,
title = {{Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance}},
author = {Mourad Grira and Hayato Miyazaki and Slim Tayachi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06404},
eprint = {2609.06404},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06404},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Threshold for the existence of scattering states for inhomogeneous nonlinear Schrödinger equations without gauge invariance
AU - Mourad Grira
AU - Hayato Miyazaki
AU - Slim Tayachi
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06404
UR - https://arxiv.org/abs/2609.06404
AB - We consider the asymptotic behavior of solutions to inhomogeneous nonlinear Schrödinger equations with non-gauge-invariant nonlinearities. The spatial coefficient in the nonlinear term may have different orders of singularity at the origin and decay at infinity. Under a coercivity condition involving the coefficient and the nonlinearity, we show that no scattering states exist for the equation below a Strauss-type threshold determined by the decay at infinity. Our class includes nonlinearities with a dominant non-oscillatory component. We also prove a complementary small-data scattering result above this threshold, using non-admissible Strichartz estimates in Lorentz spaces adapted to the singular coefficient.
ER -