加权差分格式在薛定谔方程孤立子研究中的应用

Applications of the Weighted Scheme for GNLS Equation in Solving Soliton Solutions

研究了一类高维广义非线性薛定谔方程（Ｓｃｈｒｏ¨ｄｉｎｇｅｒ方程）的孤立子解及其性质，得到了非线性参数变化（α→０ 及α→∞）时孤立子性态变化规律，同时利用加权差分格式对２维广义非线性Ｓｃｈｒｏ¨ｄｉｎｇｅｒ方程进行了研究，构造了有效的差分格式，得到了该格式稳定性和收敛性的条件，由于对非线性部分进行了适当处理。

Spatial solition solutions of class of generalized nonlinear Schr o ¨dinger equations are discussed analytically and numerically. This achieved using a travelling wave method to formulate one soliton solution and the weihted difference method to the numerical solution. The convergence and the stability have been obtained for the scheme. Numerical results obtained by the scheme are in accordance with that of analytical ones.