An integrable lattice hierarchy for Merola–Ragnisco–Tu Lattice: N-fold Darboux transformation and conservation laws

Abstract

The Lax pair of the Merola–Ragnisco–Tu (MRT) equation is derived by the prolongation technique. Then an integrable lattice hierarchy and the associated Hamiltonian structures of the hierarchy are constructed. Furthermore, the N-fold Douboux transformations for the MRT and higher-order MRT equations are established respectively, some explicit solutions of the two equations are obtained and the graphs are shown to illustrate the inelastic overtaking interactions of these soliton solutions. Finally, the infinitely many conservation laws for the MRT and higher-order MRT equations are listed.