Two new discrete integrable systems

Abstract

In this paper, we focus on the construction of new (1+1)-dimensional discrete integrable systems according to a subalgebra of loop algebra Ã1. By designing two new (1+1)-dimensional discrete spectral problems, two new discrete integrable systems are obtained, namely, a 2-field lattice hierarchy and a 3-field lattice hierarchy. When deriving the two new discrete integrable systems, we find the generalized relativistic Toda lattice hierarchy and the generalized modified Toda lattice hierarchy. Moreover, we also obtain the Hamiltonian structures of the two lattice hierarchies by means of the discrete trace identity.