广义混合非线性Schr？dinger方程的拟谱方法

本文讨论了广义混合非线性Schrodinger方程的周期初值问题,构造了守恒的半离散Fourier拟谱格式,对其近似解进行了先验估计,并证明了格式的收敛性.证明了该方程存在孤立子解,并给出其孤立子解的精确表达式.研究了线性化方程的稳定性问题,即在初值有扰动的情况下,该方程只有振荡解和鞍点.最后,通过数值例子验证了格式的可信性,数值计算表明,本格式时间方向可取大步长且是长时间稳定的,我们还计算了孤立子解,并绘出了在初值有扰动的情况下,相空间的轨线图.

THE PSEUDO-SPECTRAL FOR GENERALIZED COMPLEX NONLINEAR SCHROEDINGER EQUATION

In this paper, the author considers the generalized complex nonlinear Schroedinger equation with periodic initial value problem. A conservative semi-discrete Fourier pseudospectral scheme is proposed, where the prior estimation for the discrete system is made, the convergence of the scheme are proved. The existence of the isolated solutions is proved and the solutions to the accurate formulas are obtained. The stability of linearized eqution is discussed. Finally the credibility of the scheme is examined by numerical examples to show that the scheme is stable for a long time. The isolated solution is also checked and the orbit on the phase space is presented.