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- W3095387493 abstract "The present paper deals with the long-time asymptotic analysis of the initial value problem for the integrable defocusing nonlocal nonlinear Schrodinger equation $ iq_{t}(x,t)+q_{xx}(x,t)-2 q^{2}(x,t)bar{q}(-x,t)=0 $ with a step-like initial data: $q(x,0)to 0$ as $xto -infty$ and $q(x,0)to A$ as $xto +infty$. Since the equation is not translation invariant, the solution of this problem is sensitive to shifts of the initial data. We consider a family of problems, parametrized by $R>0$, with the initial data that can be viewed as perturbations of the shifted step function $q_{R,A}(x)$: $q_{R,A}(x)=0$ for $x<R$ and $q_{R,A}(x)=A$ for $x>R$, where $A>0$ and $R>0$ are arbitrary constants. We show that the asymptotics is qualitatively different in sectors of the $(x,t)$ plane, the number of which depends on the relationship between $A$ and $R$: for a fixed $A$, the bigger $R$, the larger number of sectors. Moreover, the sectors can be collected into 2 alternate groups: in the sectors of the first group, the solution decays to 0 while in the sectors of the second group, the solution approaches a constant (varying with the direction $x/t=const$)." @default.
- W3095387493 created "2020-11-09" @default.
- W3095387493 creator A5004114262 @default.
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- W3095387493 date "2020-09-25" @default.
- W3095387493 modified "2023-09-25" @default.
- W3095387493 title "Defocusing Nonlocal Nonlinear Schrödinger Equation with Step-like Boundary Conditions: Long-time Behavior for Shifted Initial Data" @default.
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- W3095387493 doi "https://doi.org/10.15407/mag16.04.418" @default.
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