非线性发展方程的Riemann theta函数等几种新解

Riemann theta function and other several kinds of new solutions of nonlinear evolution equations

为了构造非线性发展方程的复合型无穷序列精确解,获得了第二种椭圆方程的Riemann theta函数等几种新解.在此基础上,利用第二种椭圆方程与Riccati方程的Bcklund变换和解的非线性叠加公式,借助符号计算系统Mathematica,以mKdV方程为应用实例,构造了该方程的复合型无穷序列新精确解.这里包括Riemann theta函数、Jacobi椭圆函数、双曲函数、三角函数和有理函数,通过几种形式构成的复合型无穷序列新精确解.

Riemann theta function and other several kinds of new solutions to the second kind of elliptic equation are obtained to construct the infinite sequence complexiton solutions of nonlinear evolution equations.Based on this,applying Bcklund transformation and nonlinear superposition formula of the solutions to the second kind of elliptic equation and Riccati equation,mKdV equation is chosen as an example to seek infinite sequence new complexiton solutions with the help of symbolic computation system Mathematica,which are composed of Riemann theta function,Jacobi elliptic function,hyperbolic function,triangular function and rational function in several forms.