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
收藏
页码：893 / 952
页数：60
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