高阶非线性Schrdinger方程的自相似解

Global self-similar solutions for higher-order nonlinear Schrdinger equations

研究非线性项的形式为|u|~pu,p>0的2m阶非线性Schrdinger方程的自相似解.利用scaling和压缩映象原理证明了当初值满足一定条件时Cauchy问题解的整体存在性,据此给出了当初值的形式为U(x/(|x|))|x|^(-(2m)/p)时,自相似解的存在性.

The existence of global self-similar solutions of higher-order nonlinear Schrdinger equations with nonlinear terms |u|~pu is studied.By using a scaling technique and the Banach fixed point theorem,a general existence result is established.By using this general result to a special class of initial data,the existence of global self-similar solutions is obtained.