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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,…
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…