Backlund transformations for the second member of the first painleve hierarchy

In a recent paper (J. Math. Phys. 42 (2001) 1697) we gave a general formula tion of an algorithm introduced by Fokas and Ablowitz that allows us to obt ain Backlund transformations for nth-order ordinary differential equations, to equations of the same order but perhaps of higher degree. Here we apply this procedure to the fourth-order ordinary differential equation which is the second member of the first Painleve hierarchy. This allows us to obtai n new Backlund transformations relating this equation to other fourth-order ordinary differential equations of degrees greater than or equal to 2. (C) 2001 Elsevier Science B.V. All rights reserved.