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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.
We introduce two classes of homogeneous polynomials and show their role in constructing of integrable hierarchies for some integrable lattices.
This note is designed to show some classes of differential-difference equations admitting Lax representation which generalize evolutionary equations known in the literature.
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 ob
We consider two infinite classes of ordinary difference equations admitting Lax pair representation. Discrete equations in these classes are parameterized by two integers $kgeq 0$ and $sgeq k+1$. We describe the first integrals for these two classes
We develop a new approach to the classification of integrable equations of the form $$ u_{xy}=f(u, u_x, u_y, triangle_z u triangle_{bar z}u, triangle_{zbar z}u), $$ where $triangle_{ z}$ and $triangle_{bar z}$ are the forward/backward discrete deriva