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- Andrei K. Svinin
- 2009

which we consider as a single evolution equation on the unknown function ai ≡ a(i, x) of discrete variable i ∈ Z and continuous variable x ∈ R. For any n ≥ 1, this equation is known to be integrable… (More)

- Andrei K. Svinin
- 2011

Our main goal in this paper is to introduce two classes of homogeneous polynomials T l s and S l s of many variables and to show its applicability in the theory of integrable differential-difference… (More)

- Andrei K. Svinin
- 2004

- Andrei K. Svinin
- 2014

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… (More)

- Andrei K. Svinin
- 2002

We interpret recently suggested extended discrete KP (Toda lattice) hierarchy [1] from a geometrical point of view. We show that the latter corresponds to union of invariant submanifolds S 0 of the… (More)

- Andrei K. Svinin
- 2002

- Andrei K. Svinin
- 2011

We show that by Miura-type transformation the Itoh-Narita-Bogoyavlenskii lattice, for any $n\geq 1$, is related to some differential-difference (modified) equation. We present corresponding… (More)

- Andrei K. Svinin
- 2003

- Andrei K. Svinin
- 2005

We give an expression of polynomials for higher sums of powers of integers via the higher order Bernoulli numbers.