On a special two-dimensional lattice by Blaszak and Szum: Pfaffianization and molecule solutions

Abstract

In this paper, we first present the Casorati and grammian determinant solutions to a special two-dimensional lattice by Blaszak and Szum. Then, by using the pfaffianization procedure of Hirota and Ohta, a new integrable coupled system is generated from the special lattice. Moreover, gram-type pfaffian solutions to the pfaffianized system are proposed. Finally, the bi-directional wronskian solutions to the corresponding molecule equation are given.