Prolongation structure and integrability of the modified Sawada-Kotera equation

Abstract

Abstract The modified Sawada-Kotera equation is investigated by prolongation technique and Painlevé singularity analysis. As a result, the Lax pair and conservation laws of the modified Sawada-Kotera equation are formulated. It is proved that this equation pasts the Painlevé test in sense of having enough arbitrary functions at its resonant points. The auto-Bäcklund transformation and exact solutions of the modified Sawada-Kotera equation are obtained explicitly.