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<p>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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年11月6日

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  • Hideo Takaoka,
  • Toshihiro Tamaki

摘要

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.