Differential Invariants of Coupled Hirota-Satsuma KdV Equations

Abstract

In this paper, we consider a generalized coupled Hirota-Satsuma KdV (CHSK) system of equations. We apply the moving frames method to find a finite generating set of differential invariants for the Lie symmetry group of CHSK equations. Once the generating set of differential invariants is located, we obtain recurrence relations and syzygies among the generating differential invariants. Our approach provides a complete characterization of the structure of algebras of differential invariants of CHSK equations.