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

作　　者：韩彦江 套格图桑[1] HAN Yan-jiang;Taogetusang(College of Mathematics Science,Inner Mongolia Normal University,Huhhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院

出　　处：《数学的实践与认识》2018年第16期278-285,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11361040);内蒙古自治区自然科学基金(2015MS0128);内蒙古自治区高等学校科学研究基金(NJZY16180);内蒙古民族大学科学研究基金(NMDGP1713);内蒙古师范大学硕士研究生科研创新基金(CXJJS17075)

摘　　要：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.

关 键 词：耦合Riccati方程 非线性KLEIN-GORDON方程 函数变换 波动方程 

分 类 号：O175[理学—数学]