Research Paper#Nonlinear Schrödinger Equation, Manakov System, Asymptotics🔬 ResearchAnalyzed: Jan 3, 2026 16:37
Long-Time Asymptotics for Defocusing Manakov System
Published:Dec 26, 2025 03:03
•1 min read
•ArXiv
Analysis
This paper addresses a significant open problem in the field of nonlinear Schrödinger equations, specifically the long-time behavior of the defocusing Manakov system under nonzero background conditions. The authors provide a detailed proof for the asymptotic formula, employing a Riemann-Hilbert problem and the Deift-Zhou steepest descent analysis. A key contribution is the identification and explicit expression of a dispersive correction term not present in the scalar case.
Key Takeaways
- •Derives a long-time asymptotic formula for the defocusing Manakov system.
- •Employs a Riemann-Hilbert problem and Deift-Zhou steepest descent analysis.
- •Identifies and provides an explicit expression for a dispersive correction term not present in the scalar case.
Reference
“The leading order of the solution takes the form of a modulated multisoliton. Apart from the error term, we also discover that the defocusing Manakov system has a dispersive correction term of order $t^{-1/2}$, but this term does not exist in the scalar case...”