Comparative study of travelling wave and numerical solutions for the coupled short pulse (CSP) equation

The Lie symmetry analysis is performed for coupled short plus (CSP) equation. We derive the infinitesimals that admit the classical symmetry group. Five types arise depending on the nature of the Lie symmetry generator. In all types, we find reductions in terms of system of ordinary differential equations, and exact solutions of the CSP equation are derived, which are compared with numerical solutions using classical fourth-order Runge-Kutta scheme.