Bäcklund transformations for two new integrable partial differential equations

Area de Fisica Teórica, Facultad de Ciencias, Edificio de Fisica Universidad de Salamanca - 37008 Salamanca, Spain

Received: 22 February 1999
Accepted: 22 April 1999

Abstract

We give two new completely integrable sixth-order partial differential equations, together with their Lax pairs and Darboux transformations. From these last we are able 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 give also a linear problem for this ordinary differential equation.