孤立子与可积系统辅助求解高阶非线性薛定谔方程的可行性分析  

Feasibility Analysis of Soliton and Integrable System in Solving Higher Order Nonlinear Schrodinger Equation

作　　者：孟祥旺[1] 刘兮 MENG Xiangwang;LIU Xi(Department of Public Course Teaching,Anhui Vocational College of City Management,Hefei,Anhui 230601,China;School of Mathematics and Statistics,Hefei Normal College,Hefei,Anhui 230601,China)

机构地区：[1]安徽城市管理职业学院公共教学部,安徽合肥230601 [2]合肥师范学院数学与统计学院,安徽合肥230601

出　　处：《九江学院学报（自然科学版）》2023年第1期89-97,共9页Journal of Jiujiang University：Natural Science Edition

基　　金：安徽省高校自然科学研究项目(编号KJ2020A0120);安徽省高等学校质量工程项目(编号2021kcszsfkc017)的研究成果之一

摘　　要：文章选择变系数非线性耦合薛定谔方程作为高阶非线性薛定谔方程样例,通过达布变换求解常数系非线性耦合薛定谔方程.最后比较光超格子势阱等势阱作用下,VCNLS方程组解的动力学行为.研究表明,参数d值、h值的变化,将会引起VCNLS方程组中的亮亮孤立子解、亮暗孤立子解、怪波解的变化;势阱作用下,同一个解出现周期性变化,且形状与运动轨迹均出现变化,表明孤立子与可积系统辅助求解高阶非线性薛定谔方程具备可行性.In this study,the variable coefficient nonlinear coupled Schrodinger equation was selected as an example of high-order nonlinear Schrodinger equation,and the nonlinear coupled Schrodinger equation of constant system was solved by Darboux transformation.Finally,the dynamic behavior of the solutions of vcnls equations under the action of optical superlattice potential wells and other potential wells was compared.The results showed that the changes of parameter D and h would cause the changes of bright soliton solution,bright dark soliton solution and strange wave solution in vcnls equations;Under the action of potential well,the same solution changes periodically,and the shape and trajectory change,which showed that it was feasible to solve the higher-order nonlinear Schrodinger equation with the aid of soliton and integrable system.

关 键 词：高阶非线性薛定谔方程 孤立子 可积系统 达布变换 

分 类 号：O413[理学—理论物理]