一类广义N维非线性Schrdinger方程的孤子解及其性质研究

STUDY OF SOLITON SOLUTIONS OF A CLASS OF GENERALIZED NONLINEAR SCHRDINGER EQUATIONS IN N SPACE

研究一类Ｎ维广义非线性Ｓｃｈｒｄｉｎｇｅｒ方程的孤子解及其性质，研究非线性参数α变化（α→０及α→∞）时孤子性态的变化规律，同时研究该问题的数值解法，得到了该方程的ＰＲ差分格式的收敛性和稳定性条件．

Soliton solutions and the properties of a class of generalized nonlinear Schrdinger (GNLS) equations in N space are discussed analytically and numerically. The discussion has been done by using a travelling wave method to get one soliton solution and the finite difference method to get the numerical solutions for the GNLS equations. The states of the soliton solutions of the system admitting nonlinearity have been investigated when α→0 and α→∞ . The P R scheme for the system has been studied, and the conditions of stability and convergence for the scheme were obtained.