Nonlocal symmetries and interaction solutions of the Sawada–Kotera equation

The nonlocal symmetries of the residual symmetry and the spectral function symmetry of Sawada–Kotera (SK) equation can be derived from the truncated Painleve expansion and the Lax pair, respectively. By localizing the nonlocal symmetries of the original system to local ones of the prolonged system, the Backlund transformation and the Darboux transformation for both the original and the prolonged systems are obtained. Moreover, by the truncated Painleve expansion, we further study the integrability of the SK quation in the sense of having a consistent Riccati expansion (CRE).