摘要
给出第一种椭圆方程与函数变换相结合的方法,通过几个步骤,构造了(3+1)维Klein-Gordon方程的多种新解.步骤一、根据Jacobi椭圆函数的性质,获得了第一种椭圆方程的几种新解.步骤二、用第一种椭圆方程与函数变换相结合的方法,将(3+1)维Klein-Gordon方程的求解问题转化为非线性代数方程的求解问题.步骤三、借助符号计算系统Mathematica求出该方程组的解,并构造了由Riemannθ函数、Jacobi椭圆函数、双曲函数和三角函数两两组合的双周期解和双孤子解等多种复合型新解.
The method that combing the first kind of elliptic equation with the function transformation is presented,and by some steps,many kinds of new solutions of the(3+1)-dimension Klein-Gordon equation are constructed.Step1,according to the nature of the Jacobi elliptic function,some kinds of new solutions of the first kind of elliptic equation are obtained.Step2,by the method that combing the first kind of elliptic equation with the function transformation,the problem of solving solutions of the(3+1)-dimension KleinGordon equation is changed to the problem of solving solutions of the nonlinear algebraic equation.Step3,with the help of the symbol calculation system Mathematica,the solutions of the equation set are solved,and the two-period solutions and the two-soliton solutions and so on many kinds of new compound solutions consisting by two of Riemann θ function,Jacobi elliptic function,hyperbolic function and trigonometric function are constructed.
作者
套格图桑
伊丽娜
Taogetusang;YI Li-na(The College of Mathematical Science,Inner Mongolia Normal University,Huhhot 010022,China;Department of Mathematics,Hohhot University for Nationalities,Hohhot 010051,China)
出处
《数学的实践与认识》
北大核心
2019年第23期162-170,共9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)
