Affiliation:
1. Department of Mathematics Faculty of Civil Engineering Brno University of Technology Veveří 331/95 602 00 Brno Czech Republic
2. AdMaS Centre Faculty of Civil Engineering Brno University of Technology Purkynňova 139 612 00 Brno Czech Republic
Abstract
Abstract
The geometrical theory of partial differential equations in the absolute sense, without any additional structures, is developed. In particular the symmetries need not preserve the hierarchy of independent and dependent variables. The order of derivatives can be changed and the article is devoted to the higher-order infinitesimal symmetries which provide a simplifying “linear approximation” of general groups of higher-order symmetries. The classical Lie’s approach is appropriately adapted.
Reference12 articles.
1. Cartan, E.: Sur la structure des groupes infinis de transformations, Ann. Sci. Éc. Norm. Supér. (3) 21 (1904), 153– 206.
2. Chrastinová, V.: Report on the higher order contact transformations. 7-th Conference on Math. and Physics on Technical Universities. Proceedings part 1 – Mathematics, University of Defence, Brno, 2011.
3. Chrastinová, V.— Tryhuk, V.: Automorphisms of submanifolds, Adv. Difference Equ. 2010 (2010), Article ID 202731, 26 pp.
4. Chrastinová, V.— Tryhuk, V.: On the internal approach to differential equations 1. The involutiveness and standard basis Math. Slovaca 66 (2016), 999– 1018.
5. Chrastinová, V.— Tryhuk, V.: On the internal approach to differential equations 2. The controllability structure Math. Slovaca 67 (2017).
Cited by
1 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献