Work

On matrix Lax representations and constructions of Miura-type transformations for differential–difference equations

Year: 2024

Type: article

Abstract: This paper is part of a research project on relations between differential–difference matrix Lax representations (MLRs) with the action of gauge transformations and discrete Miura-type transformations (MTs) for (nonlinear) integrable differential–difference equations. The paper addresses the following problem: when and how can one eliminate some shifts of dependent variables from the discrete (difference) part of an MLR by means of gauge transformations? Using results on this problem, we present applications to constructing new MLRs and new integrable equations connected by new MTs to known equations. In particular, we obtain results of this kind for equations connected to the following ones: • The two-component Belov–Chaltikian lattice. • The equation (introduced by G. Marí Beffa and Jing Ping Wang) which describes the evolution induced on invariants by an invariant evolution of planar polygons. • An equation from [S. Igonin, arXiv:2405.08579 ] related to the Toda lattice in the Flaschka–Manakov coordinates.

Source: Partial Differential Equations in Applied Mathematics

DOI: 10.1016/j.padiff.2024.101014

Authors: Evgeny Chistov, Sergei Igonin

Institution: Yaroslavl State University

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,230

Funders: Ministry of Education and Science of the Russian Federation, Russian Science Foundation, Ministry of Science and Higher Education of the Russian Federation