Tri-Hamiltonian duality system of Merola-Ragnisco-Tu equation

Highlights: • The dual system of the Merola-Ragnisco-Tu equation is constructed through the approach of tri-Hamiltonian duality. • The bi-Hamiltonian structure and a linear spectral problem for the dual Merola-Ragnisco-Tu system are presented. • Darboux-Bäcklund transformation for the dual Merola-Ragnisco-Tu system has been established. • Some exact solutions for the dual Merola-Ragnisco-Tu system have been obtained. The tri-Hamiltonian method is applied to the Merola-Ragnisco-Tu equation. This enables us to construct a new integrable system, whose continuum limit is related to the AKNS system. Moreover, the system is proved to have linear spectral problems (Lax pair), bi-Hamiltonian structure and Darboux-Bäcklund transformation. Through the Darboux-Bäcklund transformation, we construct some exact solutions for the system.