Reciprocal transformations of Hamiltonian operators of hydrodynamic type: Nonlocal Hamiltonian formalism for linearly degenerate systems

DOI10.1063/1.1542921zbMath1061.37046arXivnlin/0212026OpenAlexW2020734383WikidataQ125765644 ScholiaQ125765644MaRDI QIDQ4832934

Maxim P. Pavlov, Evgeny V. Ferapontov

Publication date: 14 December 2004

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0212026

Mathematics Subject Classification ID

Related Items (18)

Loop soliton interaction in an integrable nonlinear telegraphy model: reciprocal and Bäcklund transformations ⋮ Hydrodynamic chains and the classification of their Poisson brackets ⋮ Hamiltonian structures and their reciprocal transformations for the \(r\)-KdV-CH hierarchy ⋮ Systems of conservation laws with third-order Hamiltonian structures ⋮ Integrability of the egorov systems of hydrodynamic type ⋮ Reciprocal \(F\)-manifolds ⋮ Variational bihamiltonian cohomologies and integrable hierarchies. III: Linear reciprocal transformations ⋮ The inversion symmetry of the WDVV equations and tau functions ⋮ Projective-geometric aspects of bi-Hamiltonian structures of KdV type ⋮ On classical integrability of the hydrodynamics of quantum integrable systems ⋮ Miura-reciprocal transformations and localizable Poisson pencils ⋮ Bihamiltonian systems of hydrodynamic type and reciprocal transformations ⋮ WDVV equations and invariant bi-Hamiltonian formalism ⋮ Jacobi structures of evolutionary partial differential equations ⋮ A coordinate-free construction of conservation laws and reciprocal transformations for a class of integrable hydrodynamic-type systems ⋮ Projective-geometric aspects of homogeneous third-order Hamiltonian operators ⋮ Bi-Hamiltonian aspects of a matrix Harry Dym hierarchy ⋮ Modulation of the Camassa-Holm equation and reciprocal transformations.

Cites Work

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• First-order conserved densities for gas dynamics
• On non-local Hamiltonian operators of hydrodynamic type connected with Whitham's equations
• On the local systems Hamiltonian in the weakly non-local Poisson brackets

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