Multi-solitons for the nonlinear Schr\"{o}dinger equation with repulsive Dirac delta potential
Analysis of PDEs
2023-10-16 v1
Abstract
We prove the existence of multi-soliton solutions for the nonlinear Schr\"{o}dinger equation with repulsive Dirac delta potential and -supercritical focusing nonlinear term. Our main contribution is to treat the unmoving part of the multi-solitons, which is the ground state of the equation. The linearized operator around it has two unstable eigenvalues. This is the main difference from NLS without potential, whose existence of multi-solitons is investigated by C\^{o}te, Martel, and Merle (2011).
Keywords
Cite
@article{arxiv.2310.08862,
title = {Multi-solitons for the nonlinear Schr\"{o}dinger equation with repulsive Dirac delta potential},
author = {Stephen Gustafson and Takahisa Inui and Ikkei Shimizu},
journal= {arXiv preprint arXiv:2310.08862},
year = {2023}
}