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 (1)

• Coisotropic deformations of associative algebras and dispersionless integrable hierarchies

Cited by in corpus (3)

• The dispersionless 2D Toda equation: dressing, Cauchy problem, longtime behavior, implicit solutions and wave breaking
• Quantum deformations of associative algebras and integrable systems
• Infinite hierarchies of nonlocal symmetries of the Chen--Kontsevich--Schwarz type for the oriented associativity equations