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Blow-up Solutions for Mixed Nonlinear Schrodinger Equations

作者姓名：

ShaoBinTAN

作者单位：

DepartmentofMathematics,XiamenUniversity,Xiamen361005,P.R.China

摘要：

This paper is concerned with the initial boundary-value problem for the following nonlinear evolution equation: Фt=iαФxx βФ^2Ф^-x γ|Ф|^2Фx ig(|Ф|^2)Ф Under certain conditions on the initial data and the function g(s),we study the existence and nonexistence of global solution for this equation.The blow-up solution and the blow-up time are also investigated.

关键词：

破裂解混合非线性Schroedinger方程边值问题初值问题存在性

收稿时间：

15 August 2000

Blow-up Solutions for Mixed Nonlinear Schrödinger Equations

ShaoBinTAN.Blow-up Solutions for Mixed Nonlinear Schrodinger Equations[J].Acta Mathematica Sinica,2004,20(1):115-124.

Authors:

Email author" target="_blank">Shao?Bin?Tan Email author

Institution:

(1) Department of Mathematics, Xiamen University, Xiamen, 361005, P. R. China

Abstract:

Abstract This paper is concerned with the initial boundary-value problem for the following nonlinear evolution equation:

$\phi _{t} = i\alpha \phi _{{xx}} + \beta \phi ^{2} {\mathop \phi \limits^ - }_{x} + \gamma {\left| \phi \right|}^{2} \phi _{x} + ig{\left( {{\left| \phi \right|}^{2} } \right)}\phi .$

Under certain conditions on the initial data and the function g(s), we study the existence and nonexistence of global solution for this equation. The blow-up solution and the blow-up time are also investigated. Supported by the National Science Foundation of China (No. 10071061)

Keywords:

" target="_blank"> Existence Nonexistence Blow-up Nonlinear Schr?dinger equation

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