On The Bäcklund Transformations for Cosgrove's Equation

Rama Asad Nadweh

Online Islamic University, Department Of Science and Information Technology, Doha, Qatar

Abstract

In this paper we study Bäcklund transformations (BTs) for Cosgrove’s equation F-XVIII. We use the generalization of Fokas and Ablowitz method to derive BT between F-XVIII and new fourth-order ordinary differential equations of Painlevé type. Moreover we derive auto-BT and give special solutions for F-XVIII.

Keywords: Cosgrove's equation; Backlund Transformation; Differential equation