Darboux and Bäcklund transformations of the bidirectional Sawada–Kotera equation

摘要

Darboux and Bäcklund transformations of the bidirectional Sawada–Kotera equation are derived with the help of the resulting Riccati equation. As an application, some explicit solutions of the bidirectional Sawada–Kotera equation are obtained, including rational solutions, periodic solutions, and soliton solutions.