一致分数阶导数意义下NLS方程和CNLS方程的精确解  

Exact Solutions of NLS Equations and CNLS Equations in the Sense of Conformable Fractional Derivatives

作　　者：陈进华 高云龙 CHEN Jin-hua;GAO Yun-long(School of Humanities Education,Kunming Vocational and Technical College of Industry,Anning 650300,China;School of Mathematics and Statistics,Liupanshui Normal University,Liupanshui 553004,China)

机构地区：[1]昆明工业职业技术学院人文教育学院,云南安宁650300 [2]六盘水师范学院数学与统计学院,贵州六盘水553004

出　　处：《数学的实践与认识》2022年第11期209-215,共7页Mathematics in Practice and Theory

基　　金：2019年度贵州省普通高等学校青年科技人才成长项目(黔教合KY字(2019)139,143);2020年度六盘水师范学院校级项目(LPSSYZK202002,LPSSYZK202003)。

摘　　要：在一致分数阶导数意义下,利用新的复变换研究了二阶NLS方程和CNLS方程,得到了两类带约束条件的薛定谔方程复值函数形式的新精确解.通过图像模拟,给出了两类方程的精确解在特定参数条件下随时间和空间变化的模值函数三维坐标图,实部三维坐标图和虚部三维坐标图.In the sense of conformable fractional derivative,the new complex transformation is used to study the second order NLS equation and CNLS equation,and the new exact solutions of two kinds of Schrodinger equation with constraints in the form of complex valued functions are obtained.Through simulation images,exact solutions of two classes of equations are given under the condition of certain parameters change with time and space modulus value function of the 3d coordinate diagram,real 3d coordinate diagram and the imaginary part of 3d coordinate.

关 键 词：一致分数阶导数 精确解 复变换 NLS方程 CNLS方程 

分 类 号：O175[理学—数学]