Stability of Small Solitary Waves for the One-Dimensional Nls with an Attractive Delta Potential
We consider the initial-value problem for the one-dimensional nonlinear Schrodinger equation in the presence of an attractive delta potential. We show that for sufficiently small initial data, the corresponding global solution decomposes into a small solitary wave plus a radiation term that decays and scatters as t →∞. In particular, we establish the asymptotic stability of the family of small solitary waves.
S. Masaki et al., "Stability of Small Solitary Waves for the One-Dimensional Nls with an Attractive Delta Potential," Analysis and PDE, vol. 13, no. 4, pp. 1099-1128, Mathematical Sciences Publishers (MSP), Jan 2020.
The definitive version is available at https://doi.org/10.2140/apde.2020.13.1099
Mathematics and Statistics
Keywords and Phrases
Asymptotic stability; Delta potential; NLS; Solitary waves
International Standard Serial Number (ISSN)
Article - Journal
© 2021 The Authors, All rights reserved.
01 Jan 2020