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  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.
S. Masaki et al., "ASYMPTOTIC STABILITY of SOLITARY WAVES for the 1d NLS with an ATTRACTIVE DELTA POTENTIAL," Discrete and Continuous Dynamical Systems- Series A, vol. 43, no. 6, pp. 2137 - 2185, American Institute of Mathematical Sciences (AIMS), Jun 2023.
The definitive version is available at https://doi.org/10.3934/dcds.2023006
Mathematics and Statistics
Keywords and Phrases
asymptotic stability; delta potential; NLS; scattering; soliton
International Standard Serial Number (ISSN)
Article - Journal
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01 Jun 2023