A ug 2 00 6 Dispersionless integrable equations as coisotropic deformations . Extensions and reductions
نویسنده
چکیده
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.
منابع مشابه
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 demonstra...
متن کاملCoisotropic deformations of associative algebras and dispersionless integrable hierarchies
The paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies, like the dispersionless KP and modified KP hierarchies and the universal Whitham’s hierarchy of genus zero. It stands out for the idea of interpreting these hierarchies as equations of coisotropic deformations for the structure constants of certain associative algebras. It discusses the ...
متن کاملlin / 0 60 60 69 v 1 [ nl in . S I ] 2 8 Ju n 20 06 Coisotropic deformations of associative algebras and dispersionless integrable hierarchies
The paper is an inquiry of the algebraic foundations of the theory of dispersionless integrable hierarchies, like the dispersionless KP and modified KP hierarchies and the universal Whitham’s hierarchy of genus zero. It stands out for the idea of interpreting these hierarchies as equations of coisotropic deformations for the structure constants of certain associative algebras. It discusses the ...
متن کامل00 1 ∂ - equations , integrable deformations of quasiconformal mappings and Whitham hierarchy ∗
∂-equations, integrable deformations of quasiconformal mappings and Whitham hierarchy * B. Konopelchenko Abstract It is shown that the dispersionless scalar integrable hierarchies and, in general, the universal Whitham hierarchy are nothing but classes of integrable deformations of quasiconformal mappings on the plane. Examples of deformations of quasiconformal mappings associated with explicit...
متن کاملMultidimensional integrable systems and deformations of Lie algebra homomorphisms
We use deformations of Lie algebra homomorphisms to construct deformations of dispersionless integrable systems arising as symmetry reductions of anti–self–dual Yang–Mills equations with a gauge group Diff(S). email [email protected] email [email protected] email [email protected]
متن کامل