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.
Cite this article
Pilar I Ruiz Gordoa, Andrew Pickering, Julia Prada, Integration via Modiﬁcation: A Method of Reduction of Order for Systems of Ordinary Differential Equations. Publ. Res. Inst. Math. Sci. 42 (2006), no. 1, pp. 9–26