证明一类非线性薛定谔方程存在拟周期解

Proving existence of quasiperiodic solutions of nonlinear Schrodinger equations

讨论一类薛定谔方程,首先通过Fourier展开将方程化为代数方程,再用压缩映射原理证明其存在不动点,从而原方程存在拟周期解。

we can lead to a algebraic equation by Fourier expansion for the equation β√-1）uxx＋ ε｜u｜^2 u=εF（t,x） . Furthermore, we can prove the existence of fixed point by contraction mapping theorem. As a result, quasiperioclie solutions of the equation exist.