"ASYMPTOTIC STABILITY of SOLITARY WAVES for the 1d NLS with an ATTRACTI" by Satoshi Masaki, Jason Murphy et al.
 

Abstract

We Consider the One-Dimensional Nonlinear Schrödinger Equation with an Attractive Delta Potential and Mass-Supercritical Nonlinearity. This Equation Admits a One-Parameter Family of Solitary Wave Solutions in Both the Focusing and Defocusing Cases. We Establish Asymptotic Stability for All Solitary Waves Satisfying a Suitable Spectral Condition, Namely, that the Linearized Operator Around the Solitary Wave Has a Two-Dimensional Generalized Kernel and No Other Eigenvalues or Resonances. in Particular, We Extend Our Previous Result [35] Beyond the Regime of Small Solitary Waves and Extend the Results of [19, 29] from Orbital to Asymptotic Stability for a Suitable Family of Solitary Waves.

Department(s)

Mathematics and Statistics

Comments

Japan Society for the Promotion of Science, Grant JP17H02851

Keywords and Phrases

asymptotic stability; delta potential; NLS; scattering; soliton

International Standard Serial Number (ISSN)

1553-5231; 1078-0947

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2023 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Jun 2023

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