七阶Kaup-Kupershmidt方程的经典李群分析和精确解

Classical Lie group analysis and exact solutions of the seventh-order Kaup-Kupershmidt equation

为丰富七阶Kaup-Kupershmidt(KK)方程的解,利用经典李群分析得到了七阶KaupKupershmidt(KK)方程对应的无穷小,进而得到了两种不同形式的约化方程,最后,通过对约化方程进行求解,得到了有理函数解、雅可比椭圆函数解、双曲函数解、三角函数解和幂级数解,同时,给出了幂级数解的收敛性的证明。

The classical Lie group analysis was used to obtain the corresponding infinitesimals of the seventh-order Kaup-Kupershmidt(KK)equation,and two different reduction equations were obtained.Many different forms of exact solutions of the seventh-order KK equation were achieved by solving the reduction equations,such as the rational function solution,the Jacobi elliptic function solution,the hyperbolic function solutions,the trigonometric function solutions and the power series solution,meanwhile,the convergence of the power series in the solution was proved.