一类二维非线性 Schrdinger 方程大时间问题的 Fourier 谱方法

The Fourier Spectral Method for Large Time Problem of a Class of Two-dimensional Nonlinear Schrdinger Equation

用Ｆｏｕｒｉｅｒ谱方法研究了一类二维非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程及其周期初值问题，构造了半离散的Ｆｏｕｒｉｅｒ谱逼近格式．用积分估计方法得到了离散解的一致先验积分估计，并用紧致性原理证明了连续方程大时间问题整体光滑解的存在惟一性，与半离散格式的大时间收敛性．

The Fourier spectral method for large time problem of a class of two-dimensional nonlinear schrdinger equation is studied with periodic initial value conditions.First,a semidiscrete Fourier spectral scheme is constructed,and the uniformly priori estimation of approximation solution is proved by means of integral estimate method.Furthermore,the existence and the uniquence of global smooth solution for large time problem of continuous equation are given by the compactness theorem.Finally,the long time convergence of semidiscrete scheme is proved.