基于椭圆函数展开法求Klein-Gordon方程的解  

The Solution of the Klein-Gordon Equation is Obtained Based on the Elliptic Function Expansion Method

作　　者：赵丽娟 ZHAO Lijuan(Changzhi Preschool Education College,Changzhi Shanxi 046000,China)

机构地区：[1]长治幼儿师范高等专科学校,山西长治046000

出　　处：《佳木斯大学学报（自然科学版）》2024年第8期177-180,共4页Journal of Jiamusi University：Natural Science Edition

摘　　要：非线性Klein-Gordon方程在量子场论、高能物理等领域的应用广泛,由于方程的非线性,寻找精确解已知时理论物理研究时面临的重要挑战。基于此提出一种以雅可比(Jacobi)椭圆函数展开法为基础的求解方法。通过引入雅可比椭圆函数,将非线性Klein-Gordon方程转化为可解的非线性代数方程组;同时结合雅可比椭圆函数的模数情况进行分析,分别对模数趋近极限也即模数趋近于1或者0时的情况分析非线性Klein-Gordon方程的解,最后分析当模数在正常情况下,非线性Klein-Gordon方程解的情况。旨在通过该方式更好地求解Klein-Gordon方程,为研究提供扎实基础。The nonlinear Klein-Gordon equation is widely used in quantum field theory,high-energy physics and other fields,and due to the nonlinearity of the equation,it is an important challenge in theoretical physics research to find an accurate solution.Based on this,a solution method based on the Jacobi elliptic function expansion method is proposed.By introducing the Jacobian elliptic function,the nonlinear Klein-Gordon equation is transformed into a solvable system of nonlinear algebraic equations.At the same time,combined with the analysis of the modulus of the Jacobian elliptic function,the solution of the nonlinear Klein-Gordon equation is analyzed for the modulus approach limit,that is,when the modulus is close to 1 or 0,and finally the solution of the nonlinear Klein-Gordon equation is analyzed when the modulus is under normal conditions.The aim is to better solve the Klein-Gordon equation in this way,and to provide a solid foundation for research.

关 键 词：椭圆函数 KLEIN-GORDON方程 非线性方程 椭圆函数展开法 模数 

分 类 号：O411.1[理学—理论物理]