Long-time asymptotic behavior of the modified Schrödinger equation via Dbar-steepest descent method

2019/12/21 by Yiling Yang, Yang, Yiling, Engui Fan +1
Engineering · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Optical Network Technologies

paper · pdf · doi:10.48550/arxiv.1912.10358

openalex publication_date 2019/12/21 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the Cauchy problem for the modified NLS equation. Using nonlinear steepest descent method and combining the Dbar-analysis, we show that inside any fixed cone, the long time asymptotic behavior of the solution for the modified NLS equation can be characterized with an soliton on discrete spectrum and leading order aasymptotic term on continuous spectrum up to an residual error order O(t^-3/4).

Citations

• Long-time Asymptotics for the NLS equation via dbar methods
• Global well-posedness for the derivative nonlinear Schr "odinger\n equation

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