7 citations · 13 across the 3 of their papers we have counts for
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Multi-quadratic equations associated with KdV-type equations
M. P. Kolesnikov
The potential KdV equation admits dpKdV as a full discretization. Similarly, most KdV-type equations admit multi-quadratic quad equations as algebraic condition on Bäcklund transfo…
The negative symmetry classification problem
M. P. Kolesnikov
A negative symmetry is a nonlocal symmetry of special type. In this paper, we introduce a method for constructing negative symmetries from consistent triplets of differential and d…
Non-autonomous reductions of the KdV equation and multi-component analogs of the Painlevé equations P and P
V. E. Adler, M. P. Kolesnikov
We study reductions of the Korteweg--de Vries equation corresponding to stationary equations for symmetries from the noncommutative subalgebra. An equivalent system of second-o…
Non-Abelian Toda lattice and analogs of Painlevé III equation
V. E. Adler, M. P. Kolesnikov
In integrable models, stationary equations for higher symmetries serve as one of the main sources of reductions consistent with dynamics. We apply this method to the non-Abelian tw…