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arXiv · 2008.11645

Asymptotic stability of solitary waves for the $1d$ NLS with an attractive delta potential

Satoshi Masaki·Jason Murphy·Jun-ichi Segata
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Abstract

We consider the one-dimensional nonlinear Schr\"odinger 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 beyond the regime of small solitary waves and extend the results of Fukuizumi-Ohta-Ozawa and Kaminaga-Ohta from orbital to asymptotic stability for a suitable family of solitary waves.

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Satoshi Masaki, Jason Murphy, Jun-ichi Segata. 2020-08-26. Asymptotic stability of solitary waves for the $1d$ NLS with an attractive delta potential. https://arxiv.org/abs/2008.11645

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