Large-time existence results for the nonlocal NLS around ground state solutions

Hideo Takaoka () and Toshihiro Tamaki ()
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Hideo Takaoka: Kobe University
Toshihiro Tamaki: Kobe University

Partial Differential Equations and Applications, 2025, vol. 6, issue 6, 1-23

Abstract: Abstract This paper discusses about solutions of the nonlocal nonlinear Schrödinger equation. We prove that the solution remains close to the orbit of the soliton for a large time, if the initial data is close to the ground state solitons. The proof uses the hyperbolic dynamics near ground state, which exhibits properties of local structural stability of solutions with respect to the flows of the nonlocal nonlinear Schrödinger equation.

Keywords: Nonlocal nonlinear Schrödinger equation; Large-time existence; Ground state standing waves; 35Q51; 35Q55; 42B37 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s42985-025-00360-z

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