On the asymptotic stability of N-soliton solutions of the modified nonlinear Schrödinger equation

2021/07/13 by Jin‐Jie Yang, Yang, Jin-Jie, Shou‐Fu Tian +3
Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Optical Network Technologies

paper · pdf · doi:10.48550/arxiv.2107.05836

openalex publication_date 2021/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Cauchy problem of the modified nonlinear Schrödinger (mNLS) equation with the finite density type initial data is investigated via ∂ steepest descent method. In the soliton region of space-time x/t∈(5,7), the long-time asymptotic behavior of the mNLS equation is derived for large times. Furthermore, for general initial data in a non-vanishing background, the soliton resolution conjecture for the mNLS equation is verified, which means that the asymptotic expansion of the solution can be characterized by finite number of soliton solutions as the time t tends to infinity, and a residual error \mathcal O(t^-3/4) is provided.

Citations

• Long-time Asymptotics for the NLS equation via dbar methods
• Long-time asymptotic behavior of the nonlocal nonlinear Schrödinger equation with initial potential in weighted sobolev space
• Global well-posedness for the derivative nonlinear Schr "odinger\n equation

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