一种函数变换与Klein-Gordon方程的多种新解

A Function Transformation and A Variety of New Solutions to the Klein-Gordon Equation

利用耦合Riccati方程与函数变换相结合的方法,通过几个步骤,获得了Klein-Gordon方程的多种新解.步骤一、给出一种函数变换,将Klein-Gordon方程的求解问题化为波动方程的求解问题.步骤二、利用耦合Riccati方程的解与波动方程的解,获得了Klein-Gordon方程的由双曲函数、三角函数、有理函数,及其多种形式组合的新解.步骤三、利用符号计算系统Mathematica分析了解的性质.

By combining the coupled Riccati equation with a function transformation, sev- eral new solutions of the Klein-Gordon equation are obtained through several steps. First step, the problem of solving the Klein-Gordon equation is converted to the problem of solv- ing the wave equation by a function transformation. Second step, by using the solution of coupled Riccati equation and the solution of the wave equation, the new solution through a combination of various forms to the Klein-Gordon equation is given by exponential function, trigonometric function, rational function and elliptic function. Third step, using Mathemat- ica that is the symbolic computation system analyzes the nature of solution.