Докладчик: Александр Васильевич Михайлов (Лидский университет, ЯрГУ)

Тема: PreHamiltonian difference operators, rational recursion and Hamiltonian operators for differential-difference equations (Предгамильтоновы разностные операторы, рациональная рекурсия и гамильтоновы операторы для дифференциально-разностных уравнений)

Дата:  9 октября 2019 года (среда)

Аннотация:

I am going to discuss a theory of rational (pseudo) difference recursion and Hamiltonian operators, focusing in particular  on its algebraic aspects. We represent pseudo--difference Hamiltonian operator as a ratio AB-1 of two difference operators with coefficients from a difference field F, where A is preHamiltonian. A difference operator A is called preHamiltonian if its image is a Lie subalgebra with respect to the Lie bracket of evolutionary vector fields on  F. We show that a skew-symmetric difference operator is Hamiltonian if it is preHamiltonian and satisfies simply verifiable conditions on its coefficients. If H is a rational Hamiltonian operator, then to find a second

Hamiltonian operator K compatible with H one only needs to find a preHamiltonian pair A and B such that AB-1H is skew-symmetric. Then we apply our theory to non-trivial multi-Hamiltonian structures of Narita-Itoh-Bogayavlensky and Adler-Postnikov equations.

Место:  7-й корпус ЯрГУ,  аудитория 427