Integrable hydrodynamic chains associated with Dorfman Poisson brackets
Maxim V. Pavlov
TL;DR
This paper classifies integrable Hamiltonian hydrodynamic chains linked to Dorfman Poisson brackets, deriving conservation laws, hierarchies, and associated quasilinear equations, expanding understanding of their mathematical structure and integrability.
Contribution
It introduces three main classes of integrable hydrodynamic chains with Dorfman Poisson brackets and extends hierarchies to negative moments and times.
Findings
Generated conservation laws and commuting flows.
Extended hierarchies to negative moments and times.
Derived three-dimensional quasilinear equations.
Abstract
This paper is devoted to a description of integrable Hamiltonian hydrodynamic chains associated with Dorfman Poisson brackets. Three main classes of these hydrodynamic chains are selected. Generating functions of conservation laws and commuting flows are found. Hierarchies of these Hamiltonian hydrodynamic chains are extended on negative moments and negative time variables. Corresponding three dimensional quasilinear equations of the second order are presented.
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Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Nonlinear Waves and Solitons