广义Ablowitz-Ladik方程的守恒律和Darboux变换  

Conservation Law and Darboux Transformation of Generalized Ablowitz-Ladik Equation

作　　者：谢伟康 樊方成 周冉[2] XIE Weikang;FAN Fangcheng;ZHOU Ran(School of Mathematics and Statistics,Minnan Normal University,Zhangzhou 363000,Fujian Province,China;College of Mathematics,Jilin University,Changchun 130012,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000 [2]吉林大学数学学院,长春130012

出　　处：《吉林大学学报（理学版）》2023年第2期246-250,共5页Journal of Jilin University:Science Edition

基　　金：福建省自然科学基金面上项目(批准号:2022J01892).

摘　　要：基于新的2×2离散矩阵谱问题,研究广义Ablowitz-Ladik(AL)方程的守恒律和Darboux变换.首先,利用Riccati方法给出广义AL方程的无穷守恒律,并得到其显式表示;其次,借助Lax对和规范变换构造广义AL方程的Darboux变换;最后,选择恰当的种子解,给出广义AL方程的显式精确解,得到2-扭结孤子解,并分析解的动力学性质.Based on a new 2×2 discrete matrix spectral problem,we studied conservation law and Darboux transformation of generalized Ablowitz-Ladik(AL)equation.Firstly,we gave infinite conservation law of the generalized AL equation and obtained its explicit representation by using Riccati method.Secondly,Darboux transformation(DT)of the generalized AL equation was constructed by means of the Lax pair and gauge transformation.Finally,by choosing the appropriate seed solution,we gave the explicit exact solutions of the generalized AL equation,obtained 2-kink soliton,and analyzed the dynamic properties of the solution.

关 键 词：广义Ablowitz-Ladik方程 LAX对 守恒律 DARBOUX变换 精确解 

分 类 号：O175.29[理学—数学]