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arXiv · 2310.08862

Multi-solitons for the nonlinear Schr\"{o}dinger equation with repulsive Dirac delta potential

Stephen Gustafson·Takahisa Inui·Ikkei Shimizu
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Abstract

We prove the existence of multi-soliton solutions for the nonlinear Schr\"{o}dinger equation with repulsive Dirac delta potential and $L^2$-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).

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Stephen Gustafson, Takahisa Inui, Ikkei Shimizu. 2023-10-13. Multi-solitons for the nonlinear Schr\"{o}dinger equation with repulsive Dirac delta potential. https://arxiv.org/abs/2310.08862

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