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Geometric Aspects Of Second-Order Scalar Hyperbolic Partial Differential Equations In The Plane, Martin Jurás

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

The purpose of this dissertation is to address various geometric aspects of second-order scalar hyperbolic partial differential equations in two independent variables and one dependent variable

F(x, y, u, u_x, u_y, u_xx, u_xy, u_yy) = 0

We find a characterization of hyperbolic Darboux integrable equations at level k (1) in terms of the vanishing of the generalized Laplace invariants and provide an invariant characterization of various cases in the Goursat general classification of hyperbolic Darboux integrable equations (1). In particular we give a contact invariant characterization of equations integrable by …