ar X iv : n lin / 0 60 80 10 v 2 [ nl in . S I ] 1 8 A ug 2 00 6 Dispersionless integrable equations as coisotropic deformations . Extensions and reductions

Interpretation of dispersionless integrable hierarchies as equations of coisotropic deformations for certain associative algebras and other algebraic structures is discussed. It is shown that within this approach the dispersionless Hirota equations for dKP hierarchy are nothing but the associativity conditions in a certain parametrization. Several generalizations are considered. It is demonstrated that the dispersionless integrable hierarchies of B type like the dBKP hierarchy and the dVN hierarchy represent themselves the coisotropic deformations of the Jordan’s triple systems. 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.