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

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.