Liouville integrability and explicit solutions for a Frobenius‐coupled integrable lattice hierarchy

Abstract

We define a Frobenius-coupled integrable lattice hierarchy including its Lax pair.Then the bi-Hamiltonian structures of this hierarchy are constructed, which show that this hierarchy possesses Liouville integrability. We also obtained N-fold Darboux transformation of the Frobenius-coupled integrable lattice hierarchy. Finally, the explicit solutions after onefold Darboux transformation of this hierarchy are investigated when we choose appropriate seed solutions.