Bäcklund transformations for two new integrable partial differentialequations

Abstract

We give two new completely integrable sixth-order partial differential equations,together with their Lax pairs and Darboux transformations. From these last we areable to derive the corresponding Bäcklund transformations. A simple reduction of these partial differential equations yields an integrable fourth-order ordinary differential equation for which a linear problem was previously unknown. We givealso a linear problem for this ordinary differential equation.