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Orbital stability of standing waves for defocusing fractional nonlinear Schrödinger equations with a delta potential

  • Ramón G. Plaza
  • Miguel A. Sánchez-Alcántara
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Abstract

In this paper, a fractional nonlinear Schrödinger equation with a delta potential and a repulsive nonlinearity in one space dimension is considered. First, it is proved that the Cauchy problem in Sobolev spaces on the real line is globally well-posed, independently of the sign of the delta potential. Moreover, in the case of an attractive delta potential, the existence, the minimization properties and the orbital stability of standing waves under the flow of the equation are established. The stability proof is based on concentration-compactness methods for the energy/charge functional. For that purpose, no explicit calculation of the standing waves is required and the results are based on the variational properties of the solutions alone.

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Cite

BibTeXRIS
BibTeX
@misc{plaza2026orbital,
  title = {{Orbital stability of standing waves for defocusing fractional nonlinear Schrödinger equations with a delta potential}},
  author = {Ramón G. Plaza and Miguel A. Sánchez-Alcántara},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27771},
  eprint = {2610.27771},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27771},
}
RIS
TY  - UNPB
TI  - Orbital stability of standing waves for defocusing fractional nonlinear Schrödinger equations with a delta potential
AU  - Ramón G. Plaza
AU  - Miguel A. Sánchez-Alcántara
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27771
UR  - https://arxiv.org/abs/2610.27771
AB  - In this paper, a fractional nonlinear Schrödinger equation with a delta potential and a repulsive nonlinearity in one space dimension is considered. First, it is proved that the Cauchy problem in Sobolev spaces on the real line is globally well-posed, independently of the sign of the delta potential. Moreover, in the case of an attractive delta potential, the existence, the minimization properties and the orbital stability of standing waves under the flow of the equation are established. The stability proof is based on concentration-compactness methods for the energy/charge functional. For that purpose, no explicit calculation of the standing waves is required and the results are based on the variational properties of the solutions alone.
ER  -