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Abstract: In this paper we present a far-reaching generalization of E. Vessiot-sanalysis of the Darboux integrable partial differential equations in onedependent and two independent variables. Our approach provides new insightsinto this classical method, uncovers the fundamental geometric invariants ofDarboux integrable systems, and provides for systematic, algorithmicintegration of such systems. This work is formulated within the generalframework of Pfaffian exterior differential systems and, as such, hasapplications well beyond those currently found in the literature. Inparticular, our integration method is applicable to systems of hyperbolic PDEsuch as the Toda lattice equations, 2 dimensional wave maps and systems ofoverdetermined PDE.



Autor: I.M. Anderson, M.E. Fels, P.J. Vassiliou

Fuente: https://arxiv.org/







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