SOLITON AND BLOW-UP SOLUTIONS TO THE TIME-DEPENDENT SCHRODINGER-HARTREE EQUATION

被引：52

作者：

Genev, Hristo ^{[1
]}

Venkov, George ^{[2
]}

机构：

[1] Sofia Univ St Kl Ohridski, Fac Math & Informat, Sofia, Bulgaria

[2] Tech Univ Sofia, Fac Appl Math & Informat, Sofia, Bulgaria

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2012年 / 5卷 / 05期

关键词：

Nonlinear Schrodinger equation; solitary waves; blow-up solutions; variational methods; WAVES; UNIQUENESS; EXISTENCE;

D O I：

10.3934/dcdss.2012.5.903

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the Cauchy problem for the focusing time-dependent Schrodinger - Hartree equation i partial derivative(t)psi + Delta psi = -(vertical bar x vertical bar(-(n-2)) * vertical bar psi vertical bar(alpha))vertical bar psi vertical bar(alpha-2)psi, alpha >= 2, for space dimension n >= 3. We prove the existence of solitary wave solutions and give conditions for formation of singularities in dependence of the values of alpha >= 2 and the initial data psi(0, x) =psi(0)(x).

引用

页码：903 / 923

页数：21

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