Differential invariants of Camassa–Holm equation

Abstract Under investigation in this work is a nonlinear shallow water equation, Camassa–Holm equation, which is very important in fluid dynamics, nonlinear dynamics and physical application. The new equivariant moving frames method is implemented to obtain a finite generating set of differential invariants, recurrence relations, and syzygies among the generating differential invariants, for Lie symmetry group of Camassa–Holm equation. This method is very efficient, only using the infinitesimal determining equations and choice of cross-section normalization. The results are useful support for describing the invariant properties and trend of physical, oceanic or atmospheric motion.