The Solution of the Klein-Gordon Equation is Obtained Based on the Elliptic Function Expansion Method
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 equa-tions.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 e-quation in this way,and to provide a solid foundation for research.
elliptic functionKlein-Gordon equationsnonlinear equationselliptic function ex-pansion methodmodulus
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