Backlund transformations and Darboux integrability, revisited

In a paper published in 2009, Clelland and the author proved that if a second-order hyperbolic Monge-Ampere equation in the plane is linked to the wave equation by a Backlund transformation with one-dimensional fibers, then the Monge-Ampere equation is Darboux-integrable after one prolongation. In this article, we generalize this result to pairs of hyperbolic exterior differential systems linked by such a Backlund transformation. If one system is Darboux-integrable and the other contains no closed 1-forms, then the latter system is Darboux-integrable after one prolongation. Other updates to the 2009 paper are discussed, and technical results are derived which may support further generalizations. (c) 2022 Elsevier B.V. All rights reserved.