On the Hamiltonian formalism for Korteweg-de Vries type hierarchies

DOI10.1007/BF01075282zbMath0790.58022OpenAlexW2049338953MaRDI QIDQ1316827

Vladimir Mikhalev

Publication date: 12 April 1994

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01075282

zbMATH Keywords

phase spacedual spacePoisson structuresLaurent seriesintegrable nonlinear equationsAdler-Kostant theoremKorteweg-de Vries type hierarchies

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) KdV equations (Korteweg-de Vries equations) (35Q53) Infinite-dimensional Lie (super)algebras (17B65) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35)

Related Items (25)

Kinetic equation for soliton gas: integrable reductions ⋮ A simple construction of recursion operators for multidimensional dispersionless integrable systems ⋮ Three-component nonlocal conservation laws for Lax-integrable 3D partial differential equations ⋮ Geometric structure of the classical Lagrange-d'Alembert principle and its application to integrable nonlinear dynamical systems ⋮ Lie-algebraic structure of Lax-Sato integrable heavenly equations and the Lagrange-d'Alembert principle ⋮ Integrable partial differential equations and Lie-Rinehart algebras ⋮ Unnamed Item ⋮ Multidimensional conservation laws and integrable systems II ⋮ Lax representations with non-removable parameters and integrable hierarchies of PDEs via exotic cohomology of symmetry algebras ⋮ On recursion operators for symmetries of the Pavlov-Mikhalev equation ⋮ Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I ⋮ The Lax-Sato integrable heavenly equations on functional supermanifolds and their Lie-algebraic structure ⋮ A note on the hyper-CR equation, and gauged \(N=2\) supergravity ⋮ On an integrable multi-dimensionally consistent 2 n  + 2 n -dimensional heavenly-type equation ⋮ The Cauchy problem for the Pavlov equation with large data ⋮ Integrable dispersive chains and their multi-phase solutions ⋮ Nonlinear nonisospectral differential coverings for the hyper-CR equation of Einstein-Weyl structures and the Gibbons-Tsarev equation ⋮ Integrability of exceptional hydrodynamic-type systems ⋮ Symmetries of Spectral Problems ⋮ Towards a Theory of Differential Constraints of a Hydrodynamic Hierarchy ⋮ 2D reductions of the equation u _yy = u _tx + u _yu _xx − u _xu _xy and their nonlocal symmetries ⋮ Classical M. A. Buhl problem, its Pfeiffer-Sato solutions, and the classical Lagrange-d'Alembert principle for the integrable heavenly-type nonlinear equations ⋮ Energy-dependent potentials revisited: a universal hierarchy of hydrodynamic type ⋮ Lagrangian extensions of multi-dimensional integrable equations. I: The five-dimensional Martínez Alonso-Shabat equation ⋮ Quasilinear systems of Jordan block type and the mKP hierarchy

Cites Work

• Classical r-matrices and compatible Poisson brackets for coupled KdV systems
• Kac-Moody Lie algebras and soliton equations. II: Lax equations associated with \(A_ 1^{(1)}\)
• Hamiltonian Formalism for Nonlinear SchrÖDinger Equations and Sine-Gordon Equations
• A simple model of the integrable Hamiltonian equation
• Investigation of Equations of Korteweg-De Vries Type by the Method of Recurrence Relations

This page was built for publication: On the Hamiltonian formalism for Korteweg-de Vries type hierarchies