Long-time asymptotic behavior of the nonlocal nonlinear Schrödinger equation with initial potential in weighted sobolev space

2021/01/11 by Meisen Chen, Chen, Meisen, Engui Fan +1 · 1 citation
Physics and Astronomy · Mathematics · #Quantum Mechanics and Non-Hermitian Physics #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2101.03773

Abstract

In this paper, we are going to investigate Cauchy problem for nonlocal nonlinear Schrödinger equation with the initial potential q₀(x) in weighted sobolev space H^1,1(ℝ), iq_t(x,t)amp;+q_xx(x,t)+2σq²(x,t) q(-x,t)=0, σ=±1,
q(x,0)amp;=q₀(x). We show that the solution can be represented by the solution of a Riemann-Hilbert problem (RH problem), and assuming no discrete spectrum, we majorly apply ∂-steepest cescent descent method on analyzing the long-time asymptotic behavior of it.

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