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PreprintarXiv licencearXiv

Asymptotic behavior for the damped Schrödinger equation with nonlinear dissipation

  • Takahisa Inui
  • Shun Takizawa
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Abstract

We consider large time asymptotics of solutions to the damped Schrödinger equation with the nonlinear dissipation in the mass-subcritical case. We prove that the optimal L2-decay rate of the nonlinear solution coincides with that of the corresponding linear solution even in the presence of nonlinear dissipation. Moreover, we give the optimal convergence rate for scattering for any power in the mass-subcritical regime.

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Cite

BibTeXRIS
BibTeX
@misc{inui2026asymptotic,
  title = {{Asymptotic behavior for the damped Schrödinger equation with nonlinear dissipation}},
  author = {Takahisa Inui and Shun Takizawa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07322},
  eprint = {2609.07322},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07322},
}
RIS
TY  - UNPB
TI  - Asymptotic behavior for the damped Schrödinger equation with nonlinear dissipation
AU  - Takahisa Inui
AU  - Shun Takizawa
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07322
UR  - https://arxiv.org/abs/2609.07322
AB  - We consider large time asymptotics of solutions to the damped Schrödinger equation with the nonlinear dissipation in the mass-subcritical case. We prove that the optimal L^2-decay rate of the nonlinear solution coincides with that of the corresponding linear solution even in the presence of nonlinear dissipation. Moreover, we give the optimal convergence rate for scattering for any power in the mass-subcritical regime.
ER  -