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.