基于达布变换的带三角势的Gross Pitaevskii方程的孤子解  

Soliton solutions of Gross Pitaevskii equations with trigonometric potential via Darboux transformation

作　　者：刘淑丽 张金玉[1] 李春晖 王晓丽[1] LIU Shu-li;ZHANG Jin-yu;LI Chun-hui;WANG Xiao-li(School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan 250300, China)

机构地区：[1]齐鲁工业大学(山东省科学院)数学与统计学院,山东济南250353

出　　处：《山东科学》2022年第3期115-122,共8页Shandong Science

基　　金：国家自然科学基金(11801292);山东省自然科学基金(ZR2019PA020,ZR2020MA049)。

摘　　要：研究了一类带三角势的Gross Pitaevskii方程,首先求出该方程的Lax对;其次给出该方程n次达布变换的表达式,并由此得到n孤子解;然后通过选取零种子解,求得了该方程的单孤子解和双孤子解的具体表达式。最后通过Matlab分析单孤子解和双孤子解的性质,重点讨论了参数变化对孤子的影响。Herein,a class of Gross Pitaevskii(GP)equations with a trigonometric potential is studied.First,the Lax pair of GP equations is obtained.Second,the n-th Darboux transformation of the equations is provided and the n-soliton solution is obtained.Third,by selecting a zero seed solution,specific expressions of the single soliton solution and double soliton solution of the equations are obtained.Subsequently,Matlab is used to analyze the properties of the single and double soliton solutions,focusing on the influence of changes in parameters on the soliton.

关 键 词：带三角势的Gross Pitaevskii方程 玻色-爱因斯坦凝聚 LAX对 达布变换 孤子解 

分 类 号：O24[理学—计算数学] O29[理学—数学]