This article is cited in 19 papers

Dispersionless integrable equations as coisotropic deformations: Extensions and reductions

B. G. Konopelchenko^a, F. Magri<sup>b

a</sup> Lecce University
^b Universita di Milano-Bicocca

Abstract: We discuss the interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain associative algebras and other algebraic structures. We show that with this approach, the dispersionless Hirota equations for the dKP hierarchy are just the associativity conditions in a certain parameterization. We consider several generalizations and demonstrate that B-type dispersionless integrable hierarchies, such as the dBKP and the dVN hierarchies, are coisotropic deformations of the Jordan triple systems. We show that stationary reductions of the dispersionless integrable equations are connected with dynamical systems on the plane that are completely integrable on a fixed energy level.

Keywords: associative algebra, coisotropic deformation, integrable equation.

DOI: 10.4213/tmf6058

 English version: Theoretical and Mathematical Physics, 2007, 151:3, 803–819

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