Abstract
We develop rigorously a geometric theory of third-order partial differential equations for a scalar function. Under our framework, we can define a notion of nilpotent graded Lie algebras as an invariant useful to study geometry of third-order equations. In terms of these graded Lie algebras, we provide a classification for some classes of third-order equations under a contact equivalence. By this classification, together with model equations, we also clarify several aspects for each subcategory of equations.
Funding Statement
The author was supported in part by JSPS KAKENHI (15K21058).
Acknowledgments
The author would like to express his deep gratitude to Professor Keizo Yamaguchi for constant encouragement.
Citation
Takahiro Noda. "Contact geometry of third-order partial differential equations with two independent variables." Osaka J. Math. 60 (2) 385 - 402, April 2023.
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