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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…
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)…