Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
144 tokens/sec
GPT-4o
8 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

The integrable nonlocal nonlinear Schrödinger equation with oscillatory boundary conditions: long-time asymptotics (2502.03027v1)

Published 5 Feb 2025 in math.AP

Abstract: We consider the Cauchy problem for the integrable nonlocal nonlinear Schr\"odinger equation [ \I q_{t}(x,t)+q_{xx}(x,t)+2 q{2}(x,t)\bar{q}(-x,t)=0, ] subject to the step-like initial data: $q(x,0)\to0$ as $x\to-\infty$ and $q(x,0)\simeq Ae{2\I Bx}$ as $x\to\infty$, where $A>0$ and $B\in\mathbb{R}$. The goal is to study the long-time asymptotic behavior of the solution of this problem assuming that $q(x,0)$ is close, in a certain spectral sense, to the ``step-like'' function $q_{0,R}(x)= \begin{cases} 0, &x\leq R,\ Ae{2\I Bx}, &x>R, \end{cases}$ with $R>0$. A special attention is paid to how $B\ne0$ affects the asymptotics.

Summary

We haven't generated a summary for this paper yet.