Laplace transformation of Lie class ω=1 overdetermined systems
arXiv:1108.5852 · doi:10.1142/S1402925111001805
Abstract
In this paper we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends on 1 function of 1 variable. We describe linearization of such systems and their integration via Laplace transformation, relating this to Lie's integration theorem and formal theory of PDEs.