1. Asymptotic stability of solitary waves for the $ 1d $ NLS with an attractive delta potential.
- Author
-
Masaki, Satoshi, Murphy, Jason, and Segata, Jun-ichi
- Subjects
NONLINEAR Schrodinger equation ,FAMILY stability ,SCHRODINGER equation ,EIGENVALUES - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2023
- Full Text
- View/download PDF