Bäcklund transformation of matrix equations and a discrete matrix first Painlevé equation

• DOI: 10.1016/j.physleta.2013.03.032
• Publication Date: 2013-03-28T19:03:40Z
• Authors: P.R. Gordoa; A. Pickering; Z.N. Zhu
• Keywords: 0103 physical sciences; 01 natural sciences

Abstract We show that the known auto-Backlund transformation for the matrix second Painleve equation can be generalized to a much wider class of equations. This auto-Backlund transformation is an involution and so cannot be used on its own to generate an infinite sequence of different solutions, although for particular equations a second auto-Backlund transformation allows this to be done. We also give a Backlund transformation for this general class of matrix equations. For the matrix second Painleve equation we also give a coalescence limit, and a construction of special integrals and of a discrete matrix first Painleve equation.