In this paper, the Sawada-Kotera equation is solved by using the Adomian’s decomposition method, modified Adomian’s decomposition method, variational iteration method, modified variational iteration method, homotopy perturbation method, modified homotopy perturbation method and homotopy analysis method. The approximate solution of this equation is calculated in the form of series which its comp...

In this paper, He’s variational iteration method (VIM) has been used to obtain solutions of the seventh-order Sawada-Kotera equation (sSK) and a Lax’s seventh order KdV equations(LsKdV).The numerical solutions are compared with the Adomian decomposition method(ADM) and the known analytical solutions.The work confirms the power of the VIM in reducing the size of calculations w.r.t. ADM. Some ill...

In this paper, we study explicit correspondences between the integrable Novikov and Sawada–Kotera hierarchies, and between the Degasperis–Procesi and Kaup–Kupershmidt hierarchies. We show how a pair of Liouville transformations between the isospectral problems of the Novikov and Sawada–Kotera equations, and the isospectral problems of the Degasperis–Procesi and Kaup–Kupershmidt equations relate...

This paper focuses on solving the time fractional Caudrey-Dodd-Gibbon-Sawada-Kotera equation (FCDGSKE). We propose two analytical methods based complex transform, variational iteration method and homotopy perturbation method. The approximated solutions to initial value problems associated with FCDGSKE are provided without linearization complicated calculation. Numerical results show main merits...