Dynamical properties and travelling wave analysis of Rangwala–Rao equation by complete discrimination system for polynomials

In this research, we study a variety of solutions like periodic, exponential, rational, hyperbolic and Jacobian elliptic function solutions of Rangwala–Rao equation (RRE) by employing complete discrimination system for polynomial (CDSP) technique. We deduce the relevant travelling wave system from the original equation using the travelling wave transformation and generate a conserved quantity, the Hamiltonian, from it. With the aid of qualitative theory of differential equation and bifurcation theory of planar dynamical systems a variety of phase portraits to the relevant travelling wave system of RRE are explored. The CDSP approach is not only useful for generating soliton solutions but also for carrying out qualitative analysis. Furthermore, 3D and 2D graphs are displayed for some of the soliton solutions of RRE.