The Focusing NLS Equation with Step-Like Oscillating Background: Scenarios of Long-Time Asymptotics

被引：20

作者：

Boutet de Monvel, Anne ^{[1
]}

Lenells, Jonatan ^{[2
]}

Shepelsky, Dmitry ^{[3
]}

机构：

[1] Univ Paris, Inst Math Jussieu Paris Rive Gauche, F-75205 Paris 13, France

[2] KTH Royal Inst Technol, Dept Math, S-10044 Stockholm, Sweden

[3] B Verkin Inst Low Temp Phys & Engn, 47 Nauky Ave, UA-61103 Kharkiv, Ukraine

来源：

COMMUNICATIONS IN MATHEMATICAL PHYSICS | 2021年 / 383卷 / 02期

基金：

欧洲研究理事会; 瑞典研究理事会;

关键词：

D O I：

10.1007/s00220-021-03946-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We consider the Cauchy problem for the focusing nonlinear Schrodinger equation with initial data approaching two different plane waves A(j)e(i phi j)e(-2iB)j(x), j = 1, 2 as x +/- infinity. Using Riemann-Hilbert techniques and Deift-Zhou steepest descent arguments, we study the long-time asymptotics of the solution. We detect that each of the cases B-1 < B-2, B-1 > B-2, and B-1 = B-2 deserves a separate analysis. Focusing mainly on the first case, the so-called shock case, we show that there is a wide range of possible asymptotic scenarios. We also propose a method for rigorously establishing the existence of certain higher-genus asymptotic sectors.

引用

页码：893 / 952

页数：60

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