The negative symmetry classification problem

M. P. Kolesnikov

Center of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia

Abstract: We introduce a method for constructing negative symmetries from consistent triples of differential and differential-difference equations. We also study the relation between $3$D consistent equations in the discrete and continuous case.

Keywords: recursion operator, negative flow, 3D-consistency, KdV type equation, nonlocal symmetry.

PACS: 02.30.Ik, 02.90.+p, 03.65.Fd

MSC: 35B06, 35Q53

Received: 05.04.2025
Revised: 02.05.2025

DOI: 10.4213/tmf10995

 English version: Theoretical and Mathematical Physics, 2025, 224:2, 1398–1413

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