On the local systems Hamiltonian in the weakly non-local Poisson brackets

DOI10.1016/S0167-2789(01)00280-9zbMath0991.37041arXivnlin/0006030MaRDI QIDQ5947020

Andrei Ya. Maltsev, S. P. Novikov

Publication date: 4 September 2002

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0006030

zbMATH Keywords

completely integrable soliton systemshigher symplectic structuresweakly nonlocal PB of hydrodynamic type

Mathematics Subject Classification ID

Related Items (39)

Whitham systems and deformations ⋮ Hydrodynamic chains and the classification of their Poisson brackets ⋮ Hamiltonian structures and their reciprocal transformations for the \(r\)-KdV-CH hierarchy ⋮ Hamiltonian and Lagrangian theory of viscoelasticity ⋮ Bi-Hamiltonian structure of the oriented associativity equation ⋮ Discrete exponential type systems on a quad graph, corresponding to the affine Lie algebras $A^{(1)}_{N-1}$ ⋮ Reciprocal transformations of Hamiltonian operators of hydrodynamic type: Nonlocal Hamiltonian formalism for linearly degenerate systems ⋮ Integrable hydrodynamic equations for initial chiral currents and infinite hydrodynamic chains from WZNW model and string model of WZNW type with SU(2), SO(3), SP(2), SU(∞), SO(∞), SP(∞) constant torsions ⋮ Non-local Poisson structures and applications to the theory of integrable systems ⋮ A new recursion operator for Adler's equation in the Viallet form ⋮ A nonlocal Poisson bracket of the sine-Gordon model ⋮ Weakly nonlocal Poisson brackets: tools, examples, computations ⋮ On classical integrability of the hydrodynamics of quantum integrable systems ⋮ Miura-reciprocal transformations and localizable Poisson pencils ⋮ Representations of \(\mathfrak{sl}(2,\mathbb{C})\) in category \(\mathcal{O}\) and master symmetries ⋮ On nonlocal symmetries for the Krichever-Novikov equation ⋮ Darboux transformations and recursion operators for differential-difference equations ⋮ Recursion and Hamiltonian operators for integrable nonabelian difference equations ⋮ Some remarks on the operator formalism for nonlocal Poisson brackets ⋮ On the higher Poisson structures of the Camassa-Holm hierarchy ⋮ The multi-dimensional Hamiltonian structures in the Whitham method ⋮ Recursion Operator of the Narita–Itoh–Bogoyavlensky Lattice ⋮ Nonlocal integrable PDEs from hierarchies of symmetry laws: the example of Pohlmeyer-Lund-Regge equation and its reflectionless potential solutions ⋮ A sufficient condition for a rational differential operator to generate an integrable system ⋮ Jacobi structures of evolutionary partial differential equations ⋮ Symplectic deformations of integrable field theories and AdS/CFT ⋮ ``Universal Lie algebra extensions and their Casimir invariants via commutative structures ⋮ Compatible Hamiltonian operators for the Krichever-Novikov equation ⋮ Nonlocal Hamiltonian operators of hydrodynamic type with flat metrics, integrable hierarchies, and the associativity equations ⋮ Homogeneous Hamiltonian operators and the theory of coverings ⋮ On the geometry of extended self-similar solutions of the Airy shallow water equations ⋮ A bi-Hamiltonian structure for the integrable, discrete nonlinear Schrödinger system ⋮ The Lorentz-invariant deformation of the Whitham system for the nonlinear Klein-Gordon equation ⋮ Weakly nonlocal Poisson brackets, Schouten brackets and supermanifolds ⋮ Lenard scheme for two-dimensional periodic Volterra chain ⋮ Rational recursion operators for integrable differential-difference equations ⋮ On the recursion operators for integrable equations ⋮ Modulation of the Camassa-Holm equation and reciprocal transformations. ⋮ On complete integrability of the Mikhailov–Novikov–Wang system

This page was built for publication: On the local systems Hamiltonian in the weakly non-local Poisson brackets