On the internal approach to differential equations 3. Infinitesimal\n symmetries

2014/03/04 by Veronika Chrastinová and Václav Tryhuk, Tryhuk, Veronika Chrastinová \and Václav
Engineering · Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Differential Geometry (math.DG) #FOS: Mathematics #Geotechnical and Geomechanical Engineering #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1403.0781

openalex publication_date 2014/03/04 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

The geometrical theory of partial differential equations in the absolute\nsense, without any additional structures, is developed. In particular the\nsymmetries need not preserve the hierarchy of independent and dependent\nvariables. The order of derivatives can be changed and the article is devoted\nto the higher--order infinitesimal symmetries which provide a simplifying\n"linear aproximation" of general groups of higher--order symmetries. The\nclassical Lie's approach is appropriately adapted.\n

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