Abstract
Partial differential equations have been studied much less than ordinary differential equations. Part of the theory—that of a single partial differential equation of the first order—can be reduced to the study of special ordinary differential equations, the so-called characteristic equations. This is possible because, physically speaking, non-interacting particles can be described by either the partial differential equation of the field or ordinary equations for the particles.
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© 1988 Springer Science+Business Media New York
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Arnold, V.I. (1988). First-Order Partial Differential Equations. In: Geometrical Methods in the Theory of Ordinary Differential Equations. Grundlehren der mathematischen Wissenschaften, vol 250. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1037-5_2
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DOI: https://doi.org/10.1007/978-1-4612-1037-5_2
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6994-6
Online ISBN: 978-1-4612-1037-5
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