Long time asymptotic behavior for the derivative Schrödinger equation with nonzero boundary conditions

2020/12/31 by Yang, Yiling, Cheng, Qiaoyuan, Fan, Engui
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2012.15496

Abstract

In this paper, we apply ∂ steepest descent method to study the Cauchy problem for the derivative nonlinear Schrödinger equation with nonzero boundary conditions amp;iq_t+q_xx+iσ(|q|²q)_x=0,
amp; (x,0) = q₀(x), lim_x→±∞ q₀(x) = q_±, where |q_±|=1. Based on the spectral analysis of the Lax pair, we express the solution of the derivative nonlinear Schrödinger equation in terms of solutions of a Riemann-Hilbert problem.In a fixed space-time solitonic region -3

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