Linear reciprocal transformations of bihamiltonian integrable hierarchies

Abstract: For an integrable hierarchy which possesses a bihamiltonian structure with semisimple hydrodynamic limit, we prove that the linear reciprocal transformation with respect to any of its symmetry transforms it to another bihamiltonian integrable hierarchy. Moreover, we show that the central invariants of the bihamiltonian structure are preserved under the reciprocal transformation. The main tools that we use to obtain this result are the bihamiltonian and variational bihamiltonian cohomologies defined for a bihamiltonian structure of hydrodynamic type. We also apply this result to study the problem of classification of bihamiltonian integrable hierarchies.

mathematical physicsdynamical systemsquantum algebrarepresentation theorysymplectic geometry

Audience: general audience

( slides | video )

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BIMSA Integrable Systems Seminar

Series comments: The aim is to bring together experts in integrable systems and related areas of theoretical and mathematical physics and mathematics. There will be research presentations and overview talks.

Audience: Graduate students and researchers interested in integrable systems and related mathematical structures, such as symplectic and Poisson geometry and representation theory.

The zoom link will be distributed by mail, so please join the mailing list if you are interested in attending the seminar.

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