The Hamilton-Jacobi method in the non-Hamiltonian situation and the hydrodynamic substitution

DOI10.1134/S1064562415020131zbMath1326.34066OpenAlexW797375375MaRDI QIDQ492714

V. V. Vedenyapin, N. N. Fimin

Publication date: 21 August 2015

Published in: Doklady Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1064562415020131

zbMATH Keywords

Hamilton systemsnonlinear ordinary differential equation systemstransformations for solutions

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Nonlinear ordinary differential equations and systems (34A34) Weyl theory and its generalizations for ordinary differential equations (34B20) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05)

Related Items (7)

Boltzmann and Poincaré entropy, Boltzmann extremals, and Hamilton-Jacobi method for non-Hamiltonian situation ⋮ Derivation of the equations of electrodynamics and gravity from the principle of least action ⋮ Application of the hydrodynamic substitution for systems of equations with the same principal part ⋮ Vlasov-type and Liouville-type equations, their microscopic, energetic and hydrodynamical consequences ⋮ Hydrodynamic consequences of Vlasov-Maxwell-Einstein equations and their cosmological applications ⋮ Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems ⋮ The Possibility of Introducing of Metric Structure in Vortex Hydrodynamic Systems

Cites Work

• Introduction to Hamiltonian dynamical systems and the \(N\)-body problem.
• The Liouville equation, the hydrodynamic substitution, and the Hamilton-Jacobi equation
• On the topology of steady-state solutions of hydrodynamic and vortex consequences of the Vlasov equation and the Hamilton-Jacobi method
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