导数非线性Schr dinger方程的爆破解

Blow-up solutions for derivative nonlinear Schr dinger equations

研究下述导数非线性Schrodinger方程的初边值问题:iφ_(t)+αφ_(xx)=iβ|φ|^(2σ)φx-g(|φ|^(2))φ,σ1,x∈[a,b],其中α,β为实数,g(·)是实值函数.当α,β,φ0及g(s)满足一定条件时,利用守恒律和修正的virial等式,证明了爆破解的存在性.最后,得到了爆破解的渐近行为等一些性质.

In this paper,we study the blow-up solutions to the following initial boundary value problem of the derivative nonlinear Schrodinger equations,iφ_(t)+αφ_(xx)=iβ|φ|^(2σ)φx-g(|φ|^(2))φ,σ1,x∈[a,b],whereα,βare real,g(·)is a real function.Under the some appropriate conditions onα,β,φ0 and g(s),we show the existence of the blow-up solutions by conservation laws and modified virial identity.Finally,we investigate asymptotic behavior and other properties of blow-up solutions.