Dispersionless integrable equations as coisotropic deformations. Extensions and reductions

Abstract

Interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systInterpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain algebras and other algebraic structures like Jordan triple systems is discussed. Several generalizations are considered. Stationary reductions of the dispersionless integrable equations are shown to be connected with the dynamical systems on the plane completely integrable on a fixed energy level. ems is discussed. Several generalizations are considered. Stationary reductions of the dispersionless integrable equations are shown to be connected with the dynamical systems on the plane completely integrable on a fixed energy level.

21 pages, misprints corrected

References in corpus (8)

• Integrable Hierarchies and Dispersionless Limit
• SDiff(2) KP hierarchy
• Classical $\mathbf{r}$-Matrices and Compatible Poisson Structures for Lax Equations on Poisson Algebras
• On Associativity Equations in Dispersionless Integrable Hierarchies
• Dispersionless scalar integrable hierarchies, Whitham hierarchy and the quasi-classical dbar-dressing method
• Bihamiltonian Geometry, Darboux Coverings, and Linearization of the KP Hierarchy
• Quasi-classical limit of BKP hierarchy and W-infinity symmeties
• Coisotropic deformations of associative algebras and dispersionless integrable hierarchies

Cited by in corpus (12)

• On the solutions of the second heavenly and Pavlov equations
• The dispersionless 2D Toda equation: dressing, Cauchy problem, longtime behavior, implicit solutions and wave breaking
• The Inverse Spectral Transform for the Dunajski hierarchy and some of its reductions, I: Cauchy problem and longtime behavior of solutions
• Solvable vector nonlinear Riemann problems, exact implicit solutions of dispersionless PDEs and wave breaking
• Integrable dispersionless PDEs arising as commutation condition of pairs of vector fields
• Quantum deformations of associative algebras and integrable systems
• Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations
• Dispersionful analogue of the Whitham hierarchy
• Coisotropic deformations of algebraic varieties and integrable systems
• Discrete integrable systems and deformations of associative algebras
• Continuous-discrete integrable equations and Darboux transformations as deformations of associative algebras
• Cohomological, Poisson structures and integrable hierarchies in tautological subbundles for Birkhoff strata of Sato Grassmannian