2 citations · 3 across the 9 of their papers we have counts for
9 papers
Computational Algorithms for Invariant Reduction of Variational Forms
Kostya Druzhkov, Alexey Shevyakov
Symmetry reductions of partial differential equations (PDEs) inherit more geometric structures than other types of reductions: invariant conservation laws, variational structures,…
Invariant Reduction for Partial Differential Equations. IV: Symmetries that Rescale Geometric Structures
Kostya Druzhkov, Alexei Cheviakov
For a system of partial differential equations admitting point, contact, or higher symmetries, the framework of invariant reduction systematically computes how invariant geometric…
Invariant Reduction for Partial Differential Equations. III: Poisson Brackets
Kostya Druzhkov
We show that, under suitable conditions, finite-dimensional systems describing invariant solutions of partial differential equations (PDEs) inherit local Hamiltonian operators thro…
A non-trivial conservation law with a trivial characteristic
Kostya Druzhkov
We show that the conservation law of the overdetermined system , , associated with the characteristic , is non-trivial despite the…
Invariant Reduction for Partial Differential Equations. II: The General Framework
Kostya Druzhkov, Alexei Cheviakov
For a system of partial differential equations (PDEs) admitting a local (point, contact, or higher) symmetry with the characteristic , invariant solutions satisfy th…
Invariant Reduction for Partial Differential Equations. I: Conservation Laws and Systems with Two Independent Variables
Kostya Druzhkov, Alexei Cheviakov
For a system of partial differential equations that has an extended Kovalevskaya form, a reduction procedure is presented that allows one to use a local (point, contact, or higher)…
Internal Lagrangians and spatial-gauge symmetries
Kostya Druzhkov
A direct reformulation of the Hamiltonian formalism in terms of the intrinsic geometry of infinitely prolonged differential equations is obtained. Concepts of spatial equation and…
Internal Lagrangians of PDEs as variational principles
Kostya Druzhkov
A description of how the principle of stationary action reproduces itself in terms of the intrinsic geometry of variational equations is proposed. A notion of stationary points of…
Lagrangian formalism and the intrinsic geometry of PDEs
Kostya Druzhkov
A notion of internal Lagrangian for a system of differential equations is introduced. A spectral sequence related to internal Lagrangians is obtained. A connection between internal…