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Register a new userOn some class of homogeneous polynomials and explicit form of integrable hierarchies of differential-difference equations
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Added by
Andrei Svinin Kirillovich
Publication date
2011
fields
Physics
and research's language is
English
Authors
Andrei K. Svinin
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We introduce two classes of homogeneous polynomials and show their role in constructing of integrable hierarchies for some integrable lattices.
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In this paper we show that an arbitrary solution of one ordinary difference equation is also a solution for infinite class of difference equations. We also provide an example of such a solution that is related to sequence generated by second-order linear recurrent relations.
This note is designed to show some classes of differential-difference equations admitting Lax representation which generalize evolutionary equations known in the literature.
We introduce two classes of discrete polynomials and construct discrete equations admitting a Lax representation in terms of these polynomials. Also we give an approach which allows to construct lattice integrable hierarchies in its explicit form and show some examples.
A class of multidimensional integrable hierarchies connected with commutation of general (unreduced) (N+1)-dimensional vector fields containing derivative over spectral variable is considered. They are represented in the form of generating equation, as well as in the Lax-Sato form. A dressing scheme based on nonlinear vector Riemann problem is presented for this class. The hierarchies connected with Manakov-Santini equation and Dunajski system are considered as illustrative examples.
We show some classes of higher order partial difference equations admitting a zero-curvature representation and generalizing lattice potential KdV equation. We construct integrable hierarchies which, as we suppose, yield generalized symmetries for obtained class of partial difference equations. As a byproduct we also derive non-evolutionary differential-difference equations with their Lax pair representation which may be of potential interest.
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