# Long-time asymptotics for the integrable nonlocal nonlinear Schrödinger equation

@article{Rybalko2017LongtimeAF,
title={Long-time asymptotics for the integrable nonlocal nonlinear Schr{\"o}dinger equation},
author={Yan Rybalko and Dmitry Shepelsky},
journal={Journal of Mathematical Physics},
year={2017}
}
• Published 22 October 2017
• Mathematics
• Journal of Mathematical Physics
We study the initial value problem for the integrable nonlocal nonlinear Schrodinger (NNLS) equation iqt(x,t)+qxx(x,t)+2σq2(x,t) q¯ (−x,t)=0 with decaying (as x → ±∞) boundary conditions. The main aim is to describe the long-time behavior of the solution of this problem. To do this, we adapt the nonlinear steepest-decent method to the study of the Riemann-Hilbert problem associated with the NNLS equation. Our main result is that, in contrast to the local NLS equation, where the main asymptotic…

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