Focusing singularity in a derivative nonlinear Schrodinger equation

被引：19

作者：

Liu, Xiao ^{[1
]}

Simpson, Gideon ^{[2
]}

Sulem, Catherine ^{[1
]}

机构：

[1] Univ Toronto, Dept Math, Toronto, ON M5S 1A1, Canada

[2] Univ Minnesota, Sch Math, Minneapolis, MN 55455 USA

来源：

PHYSICA D-NONLINEAR PHENOMENA | 2013年 / 262卷

基金：

加拿大自然科学与工程研究理事会; 美国国家科学基金会;

关键词：

Derivative nonlinear Schrodinger equation; Blowing-up solutions; Rate of blow-up; Dynamic rescaling; WELL-POSEDNESS; MODULATION;

D O I：

10.1016/j.physd.2013.07.011

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a numerical study of a derivative nonlinear Schrodinger equation with a general power nonlinearity, vertical bar psi vertical bar(2 sigma) psi(x). In the L-2-supercritical regime, sigma > 1, our simulations indicate that there is a finite time singularity. We obtain a precise description of the local structure of the solution in terms of the blowup rate and the asymptotic profile, in a form similar to that of the nonlinear Schrodinger equation with supercritical power law nonlinearity. (C) 2013 Elsevier B.V. All rights reserved.

引用

页码：48 / 58

页数：11

共 20 条

[1]

[Anonymous], 2006, NONLINEAR FIBER OPTI

[2] Singular solutions of the L2-supercritical biharmonic nonlinear Schrodinger equation [J].