Some exact solutions of (1+1)-dimensional Kaup-system and seventh-order Kawahara equation

In this paper, we solve a $(1+1)$-dimensional Kaup system and seventh order Kawahara equation. The Lie symmetry analysis is used to perform the similarity reduction and to obtain the exact solutions of the $(1+1)$ dimensional Kaup system and seventh order Kawahara equation. Similarity transformation method reduces $(1+1)$-dimensional Kaup system into a system of ODEs and nonlinear Kawahara equation into nonlinear ordinary differential equation (ODE) and helps to find exact solutions. With the help of reduction equations, we have obtained the exact explicit solutions. Moreover, later by power series method, the exact analytic solutions for seventh order Kawahara equation are obtained.