分数阶及整数阶Klein-Gordon方程的孤立波解研究  

Research of Solitary Wave Solutions for Fractional-Order and Integer-Order Klein-Gordon Equations

作　　者：陆求赐[1] 张宋传 王学彬 徐瑞标[1] LU Qiu-ci;ZHANG Song-chuan;WANG Xue-bin;XU Rui-biao(School of Humanities and Teachers Education,Wuyi University,Wuyishan 354300,China;School of Mathematics and Computer,Wuyi University,Wuyishan 354300,China)

机构地区：[1]武夷学院人文与教师教育学院,福建武夷山354300 [2]武夷学院数学与计算机学院,福建武夷山354300

出　　处：《数学的实践与认识》2023年第3期263-270,共8页Mathematics in Practice and Theory

基　　金：福建省教育厅科技项目(JA15512,JAT160519);福建省科技厅项目(2021J011148);高级引进人才科研启动项目(YJ201802)。

摘　　要：Klein-Gordon方程是量子力学领域的一类重要方程,它是薛定谔方程的一种相对论形式,包括分数阶和整数阶方程,寻求它的解有着重要的意义.利用一种较为实用的1/G展开法,对一类分数阶Klein-Gordon方程和相应的整数阶Klein-Gordon方程进行了求解,得到了丰富的行波解,包括孤立波解和扭曲波解,同时有代表性地选择一些解,来画出它们的图形并进行相图分析.另外,对所得到的整数阶与分数阶方程的解进行了对比,发现了它们的异同点.Klein-Gordon equation is an important equation in the field of quantum mechanics,it is a relativistic form of Schrodinger equation which includes fractional-order and integerorder equations and it is of great significance to seek its solutions.In this paper,we take a useful 1/G expansion method to solve a kind of fractional-order Klein-Gordon equation and the corresponding integer-order Klein-Gordon equation and obtain abundant travelling wave solutions which include solitary wave solutions and distorted wave solutions.In the same time,we choose some solutions typically to draw their graphs and analyze phase diagrams.In addition,we compare the solutions of fractional-order and integer-order equations and find their similarities and differences.

关 键 词：分数阶Klein-Gordon方程 整数阶Klein-Gordon方程 1/G展开法 行波变换 孤立波解 扭结波解 

分 类 号：O175[理学—数学]