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Geometric aspects of S-integrability
This is a report on results on zero-curvature representations and Bäcklund transformations of S-integrable partial differential equations recently obtained within the framework of the Vinogradov diffiety theory....
BA - Obecná matematika
- 2000 •
- D
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D - Stať ve sborníku
Jets
Jets is a set of Maple procedures to facilitate solution of differential equations in total derivatives on diffieties. Otherwise said, Jets is a tool to compute symmetries, conservation laws, zero-curvature representations, recursion operato...
BA - Obecná matematika
- 2009 •
- R
Rok uplatnění
R - Software
On the internal approach to differential equations, 2. The controllability structure
The article concerns the geometrical theory of general systems of PDEs without any additional structure and subject to arbitrary change of variables.
Pure mathematics
- 2017 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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The symmetry reduction of variational integrals
The Routh reduction of cyclic variables in the Lagrange function and the Jacobi-Maupertuis principle of constant energy systems are generalized...
Pure mathematics
- 2018 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
Jets 5.81
Jets is a set of Maple procedures to facilitate solution of differential equations in total derivatives on diffieties. Otherwise said, Jets is a tool to compute symmetries, conservation laws, zero-curvature representations, recursion operato...
BA - Obecná matematika
- 2014 •
- R •
- Link
Rok uplatnění
R - Software
Výsledek na webu
On the internal approach to differential equations 3. Infinitesimal symmetries
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 derivat...
Pure mathematics
- 2016 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Automorphisms of Ordinary Differential Equations
The paper deals with the local theory of internal symmetries of underdetermined systems of ordinary differential equations in full generality. The symmetries need not preserve the choice of the independent variable, the hierarchy of dependent variabl...
Pure mathematics
- 2014 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
Report on the Absolute Differential Equations I
The article provides a survey of the absolute theory of general systems of (partial) differential equations. The equations are relieved of all additional structures and subject to quite arbitrary change of the variables. An abstract mathematical theo...
Pure mathematics
- 2017 •
- Jost •
- Link
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Jost - Ostatní články v recenzovaných periodicích
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The Poincaré-Cartan forms of one-dimensional variational integrals
Fundamental concepts for variational integrals evaluated on the solutions of a system of ordinary differential equations are revised. The variations, stationarity, extremals and especially the Poincare-Cartan differential forms are relieved of all ad...
Pure mathematics
- 2020 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
Výsledek na webu
The Lie Group in Infinite Dimension
A Lie group acting on finite-dimensional space is generated by its infinitesimal transformations and conversely, any Lie algebra of vector fields in finite dimension generates a Lie group (the first fundamental theorem). This classical result is adju...
BA - Obecná matematika
- 2011 •
- Jx
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
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