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The symmetry reduction of variational integrals, complement
Some open problems appearing in the primary article on the symmetry reduction are solved.
Pure mathematics
- 2018 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Applications of solvable structures to the nonlocal symmetry-reduction of ODEs
An application of solvable structures to the reduction of ODEs with a lack of local symmetries is given. Solvable structures considered here are all defined in a nonlocal extension, or covering space, of a given ODE. Examples of the...
BA - Obecná matematika
- 2009 •
- D
Rok uplatnění
D - Stať ve sborníku
2D reductions of the equation u_{yy} = u_{tx} + u_{y}u_{xx} - u_{x}u_{xy} and their nonlocal symmetries
symmetry reductions: (1) u_{yy} = (u_y + y) u_{xx} - u_{x} u_{xy} - 2 (which}) u{xy} - u_{x}. Using the corresponding reductions of the known Lax pair for the 3D equation, we describe nonlocal symmetries of (1) an...
Pure mathematics
- 2017 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Reductions of the Universal Hierarchy and rdDym Equations and Their Symmetry Properties
We consider the equations u_{yy}= u_y u_{xx} - (u_x+ u) u_{xy} + u_x u_y , u_{yy} = (u_x+ x) u_{xy} - (u_{xx} + 2) u_y that arise as reductions of the universal hierarchy and rdDym equations, respectively, and describe the Lie algebras of no...
Pure mathematics
- 2018 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Symmetry reduction and recovery of trajectories of optimal control problems via measure relaxations
We address the problem of symmetry reduction of optimal control problems under the action of a finite group from a measure relaxation viewpoint. We propose a method based on the moment-Sum of Squares (SOS) aka Lasserre hierarchy whi...
Applied mathematics
- 2024 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Lie reductions and exact solutions of dispersionless Nizhnik equation
We exhaustively classify the Lie reductions of the real dispersionless Nizhnik differential equations. Lie and point symmetries of reduced equations are comprehensively studied, including the analysis of which of them correspond to ...
Pure mathematics
- 2024 •
- Jimp •
- Link
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Jimp - Článek v periodiku v databázi Web of Science
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Utiyama's reduction method and infinitesimal symmetries of invariant Lagrangians
We generalize the Utiyama reduction method for invariant Lagrangians of gravitational and gauge fields and describe infinitesimal symmetries of such Lagrangians......
BA - Obecná matematika
- 2007 •
- D
Rok uplatnění
D - Stať ve sborníku
On the Routh reduction of variational integrals. Part 1: The classical theory.
A geometrical approach to the reductions of one-dimensional first order variational integrals with respect to a Lie symmetry group is discussed. The method includes both the Routh reduction of cyclic variables and the Jacob...
BA - Obecná matematika
- 2012 •
- Jx
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Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Discrete symmetries and supersymmetries - powerful tools for studying quantum-mechanical systems
This invited talk briefly summarized the recent results of Prof. A. Nikitin and the author concerning discrete symmetries and supersymmetries of various quantum-mechanical systems......
BF - Elementární částice a fyzika vysokých energií
- 1999 •
- D
Rok uplatnění
D - Stať ve sborníku
Integrability properties of some equations obtained by symmetry reductions
In our recent paper [1], we gave a complete description of symmetry reduction of four Lax-integrable (i.e., possessing a zero-curvature representation with a non of the integrability features of the initial equations under the r...
BA - Obecná matematika
- 2015 •
- Jx •
- Link
Rok uplatnění
Jx - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)
Výsledek na webu
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