Bäcklund transformations for fifth–order Cosgrove’s equations

Abstract

In this article we use a generalization of Fokas and Ablowitz algorithm to obtain Baecklund transformations (BTs) for the fifth-order ordinary differential equations of Cosgrove, Fif-Fif-II, Fif-III, and FifIV. We derive BTs between the equations Fif-I...., Fif-IV and new Painleve-type equations of the same order and higher degree. The form of some of the new equations are also given.