Two-Field Integrable Evolutionary Systems of the Third Order and Their Differential Substitutions

2008/02/09 by A. G. Meshkov, Anatoly G. Meshkov, Maxim Ju. Balakhnev · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.3842/sigma.2008.018

published as SIGMA 4 (2008), 018, 29 pages · Published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

arxiv created 2008/02/09 · openalex publication_date 2008/02/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

A list of forty third-order exactly integrable two-field evolutionary systems is presented. Differential substitutions connecting various systems from the list are found. It is proved that all the systems can be obtained from only two of them. Examples of zero curvature representations with 4 4 matrices are presented.

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• On matrix Lax representations for (1+1)-dimensional evolutionary differential-difference equations

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