分数阶Klien-Fock-Gordon方程精确解的构建  

Construction of Solutions of Fractional Order Klien⁃Fock⁃Gordon Equation

作　　者：黄宣聪 孙峪怀 肖思宇 HUANG Xuancong;SUN Yuhuai;XIAO Siyu(School of Mathematical Sciences,Sichuan Normal University,Chengdu 610066,China)

机构地区：[1]四川师范大学数学科学学院,四川成都610066

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2023年第4期399-406,共8页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(12071323)。

摘　　要：首先利用整合分数阶导数和分数阶复变换将非线性时空分数阶Klien-Fock-Gordon方程转化为常微分方程,然后再应用广义G′/(G′+G+A)展开法得到该方程新精确解。取特定参数值,得到各种特殊类型解,如扭结波解、奇异波解、周期波解、三角函数解。其中解q_(1)(x,t)~q_(4)(x,t)不同于已有文献,该方法丰富了分数阶Klien-Fock-Gordon方程的解,从而也表明广义G′/(G′+G+A)展开法对分数阶偏微分方程精确解的研究具有意义。The solutions of fractional order Klien‐Fock‐Gordon equation were constructed in the paper.Firstly,the cubic nonlinear space‐time fractional order KlienFock‐Gordon equation was transformed into an ordinary differential equation through integrating fractional derivative and fractional complex transformation.And then,a new exact solution of the equation was obtained by the generalized G′/(G′+G+A)‐expansion method.When the special parameter values were set,various special types of solutions were obtained,such as kink wave solutions,singular wave solutions,periodic wave solutions,and trigonometric function solutions,of which the solution q_(1)(x,t)~q_(4)(x,t)was different from the existing literature.The application of this method enriched the solution of fractional order Klien‐Fock‐Gordon equation,and also showed that the generalized G′/(G′+G+A)‐expansion method was universal for solving the exact solution of fractional order partial differential equation.

关 键 词：分数阶导数 分数阶Klien-Fock-Gordon方程 广义G′/(G′+G+A)展开法 精确解 

分 类 号：O175.29[理学—数学]