Soliton molecules, nonlocal symmetry and CRE method of the KdV equation with higher-order corrections

Abstract

The soliton molecules of the Korteweg–de Vries (KdV) equation with higher-order corrections are studied by using the velocity resonance mechanism and the multi-soliton solution. The interaction between a soliton molecule and one-soliton of the KdV equation with higher-order corrections is elastic by means of analytical and graphical ways. The nonlocal symmetry of the KdV equation with higher-order corrections is derived by the truncate Painlevé analysis. An nonauto-Bäcklund theorem is established by solving the initial value problem of the Lie’s first principle of the nonlocal symmetry. In the meanwhile, the KdV equation with higher-order corrections is proved to be a consistent Riccati expansion (CRE) solvable system by exploiting the CRE method.