非线性Schr?dinger方程的驻波解

Stationary Solutions of a Kind of Nonlinear Schr?dinger Equations

本文研究等离子体中的高功率超短激光通道问题中出现的一类非线性Schr?dinger方程,利用变分原理,把一类非线性Schr?dinger方程转换为变分问题,再利用喷泉定理及对偶喷泉定理证明一类非线性Schr?dinger方程存在驻波解.

This paper studied a class of nonlinear Schr？dinger equation from high power ultrashort laser in the plasma channel problem. Using the variational principle, a class of nonlinear Schr？dinger equations is converted into a variational problem. Using fountain theorem and dual fountain theorem, proving a class of nonlinear Schr？dinger equation have stationary solutions.