The Fundamental Theorem of Tropical Partial Differential Algebraic Geometry

Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of Tropical Differential Algebraic Geometry states that the suppor...

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Bibliographic Details
Published inarXiv.org
Main Authors Falkensteiner, Sebastian, Garay-López, Cristhian, Haiech, Mercedes, Noordman, Marc Paul, Toghani, Zeinab, Boulier, François
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 07.02.2020
Subjects
Algebra
Differential geometry
Geometry
Ordinary differential equations
Partial differential equations
Power series
Theorems
Vertex sets
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Summary:Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input. The Fundamental Theorem of Tropical Differential Algebraic Geometry states that the support of solutions of systems of ordinary differential equations with formal power series coefficients over an uncountable algebraically closed field of characteristic zero can be obtained by solving a so-called tropicalized differential system. Tropicalized differential equations work on a completely different algebraic structure which may help in theoretical and computational questions. We show that the Fundamental Theorem can be extended to the case of systems of partial differential equations by introducing vertex sets of Newton polygons.
ISSN:2331-8422