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

The Fourier spectral mehod for large time problem of a class of two-dimensional nonlinear Schrodinger equations (Ⅱ)

用Ｆｏｕｒｉｅｒ谱方法讨论如下的非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程及其周期初值问题 ｕｔ－（λ十ｉａ）Δｕ＋（ｋ＋ｉβ）ｕ~2ｕ+γｕ＝ｆ（ｘ，ｔ），ｕ（ｘ＋２π，ｔ），ｕ（ｘ，０）＝ｕ_０（ｘ） 构造了全离散的Ｆｏｕｒｉｅｒ谱逼近格式，并证明了格式的大时间收敛性。

The authors study the Fourier spectral method for large time problem of a class of two-dimensional nonlinear Schrodinger equations with periodic initial value conditions of following u_t-(λ+ia)△u +(k +iβ)u^2u +γu=f(x, t), u(x + 2π, t) = u(x, t), u(x, 0) = u_0(x)。 A fully discrete Fourier spectral scheme is constructed, and the long time convergence of scheme is proved.