Integration via Modification: A Method of Reduction of Order for Systems of Ordinary Differential Equations

Abstract

We give a method of reduction of order for systems of ordinary differential equations having a certain structure. Our method is based on establishing a Bäcklund transformation between an integrated modified system and an integrated version of the system under consideration. The originality of our approach lies in the application of ideas more familiar within the context of completely integrable partial differential equations to the question of reduction of order of ordinary differential equations, whether these last be integrable or not.