具调和振子的非线性Schr dinger方程的Cauchy问题

Cauchy Problem of Nonlinear Schr dinger Equations with Harmonic Oscillator

考虑具调和振子的非线性 Schr dinger方程的 Cauchy问题 .采用 Galerkin方法证明了整体强解的存在性 。

The Cauchy problem for the nonlinear Schrodinger equations with harmonic oscillator is considered. By the Galerkin expansion procedure and the eigenfunctions of the harmonic oscillator, it is shown that the nonlinear initial value problem in one dimension space has a unique global strong solution as long as the initial wave function Ψ 0 belongs to certain function space.