Existence of Global Solutions to the Derivative NLS Equation with the Inverse Scattering Transform Method

被引：56

作者：

Pelinovsky, Dmitry E. ^{[1
]}

Shimabukuro, Yusuke ^{[2
]}

机构：

[1] McMaster Univ, Dept Math & Stat, Hamilton, ON L8S 4K1, Canada

[2] Acad Sinica, Inst Math, Taipei 10617, Taiwan

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2018年 / 2018卷 / 18期

基金：

加拿大自然科学与工程研究理事会;

关键词：

NONLINEAR SCHRODINGER-EQUATION; WELL-POSEDNESS; SOLITARY WAVES; STABILITY; ASYMPTOTICS; SOLITONS;

D O I：

10.1093/imrn/rnx051

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We address the existence of global solutions to the derivative nonlinear Schrodinger (DNLS) equation without the small-norm assumption. By using the inverse scattering transform method without eigenvalues and resonances, we construct a unique global solution in H-2(R) boolean AND H-1,H-1(R) which is also Lipschitz continuous with respect to the initial data. Compared to the existing literature on the spectral problem for the DNLS equation, the corresponding Riemann-Hilbert problem is defined in the complex plane with the jump on the real line.

引用

页码：5663 / 5728

页数：66

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