本文首先应用Adomian分解法给出了横向非周期调制的五次非线性薛定谔方程的精确孤子解,并将其同数值结果进行了比较,它们吻合得很好。进而针对不同介质的传播常数k研究了精确解的线性稳定性和非线性稳定性,k<1.724时孤子解不稳定,1.724≤k<2.264时其具有非线性稳定性,但是不具有线性稳定性;k≥2.264时孤子解既是非线性稳定的,也是线性稳定的。

An exact soliton solution for quintic-nonlinear Schrdinger equation with a type of transverse nonperiodic modulation was studied by using of the Adomian decomposition method in this paper.After the comparison of the analytical solution with the numerical solution,We found that they were in good agreement.Then we investigated the linear and nonlinear stability property of the exact solution for different propagation constant k in nonlinear medium. The soliton solution was unstable for k<1.724. It had the nonlinear stability,but did not have linear stability for 1.724≤k<2.264. But it had the linear and nonlinear stability for k≥2.264.