Abundant travelling wave solutions for KdV–Sawada–Kotera equation with symbolic computation

New interaction solutions of the KdV-Sawada-Kotera-Ramani equation in various dimensions

“…Through the generalized auxiliary equation method, many new exact solutions to equation (1) are obtained including Jacobi elliptic function solutions, the Weierstrass elliptic function solutions and rational solutions [26]. Solitary wave solutions, periodic and quasi-periodic traveling wave solutions are constructed by reducing the KdVSKR equation into two systems of ordinary differential equation [27].…”

Dispersive Traveling Wave Solution for Non-Linear Waves Dynamical Models

“…In recent years, study of these two equations has been done to obtain the exact solution using different methods. Methods of obtaining analytical or exact solution to the gKdv and Ske nonlinear partial differential equations used by other researchers include the sine-cosine method [1], an auto-Blackland transformation [2], Hirota direct method [3], the projective Riccati equation method [4], the He's varia-tional method [5], the Hirota bilinear method [6], the symbolic computation method [7] [8], the Odd Hamiltonian structure [9], the extended tanh method [10], (G'/G)-expansion method [11], the sub-ODE method [12], the extended mapping method [13], the tanh-coth method [14], etc. The simple equation method for solving nonlinear partial differential equations has gained a lot of attention from researchers due to its simplicity and ability to extract novel traveling wave solutions.…”

Meromorphic solutions of nonlinear ordinary differential equations

“…Zhang with co-authors [24] obtained 20 travelling wave solutions for the KdV-Sawada-Kotera equation. However the nonlinear ordinary differential equation corresponding to the KdV -Sawada -Kotera equation was studied many years ago.…”