摘要
将直接微扰方法应用于含时间色散项的耦合非线性薛定谔方程来获得该微扰方程的包含零阶和一阶修正的解析近似解,并借此近似解分析了微扰项对孤子的各个参数的影响.特别地,通过楼森岳的直接微扰方法能同时得到方程的各种不同形式的微扰解,包括单孤子解、双孤子解甚至N孤子解等.为了进一步检验直接微扰方法的有效性,还对微扰耦合非线性薛定谔方程进行了数值求解.结果表明,当微扰参数足够小时,解析解与数值解符合得相当好.
The approximate solutions to the coupled nonlinear Schrtidinger equation with a small time-dispersion were obtained by means of Lou＇s direct perturbation method. The effect of perturbations on the soliton parameters were analyzed in details based on the reliable approximate solutions. Furthermore, by Lou＇s direct perturbation method, different types of perturbation solution of nonlinear evolution equations could also be derived, including the single-soliton solution, two-soliton solutions and even the N-soliton solutions as ＇well. So the perturbation solutions obtained by Lou＇s direct perturbation method were showed to be more abundant than those by other methods. In order to check the availability of the direct perturbation method, the PCNLSE were solved directly as an example, it turned out that the approximate analytical solutions of PCNLSE agreeed well with the numerical solutions within a wide range of values.
出处
《浙江师范大学学报（自然科学版）》
CAS
2007年第4期361-367,共7页
Journal of Zhejiang Normal University:Natural Sciences
基金
国家自然科学基金资助项目(10575087)
浙江省自然科学基金资助项目(102053)
关键词
直接微扰方法
微扰
耦合非线性薛定谔方程
近似解
direct perturbation method
perturbation
N-component nonlinear Schr^dinger equation
asymp-totical solution
