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arxiv: 0802.1253 · v1 · submitted 2008-02-09 · 🌊 nlin.SI · math-ph· math.MP

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

Anatoly G. Meshkov , Maxim Ju. Balakhnev
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classification 🌊 nlin.SI math-phmath.MP
keywords systemsdifferentialevolutionaryintegrablelistpresentedsubstitutionstwo-field
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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 $4 \times 4$ matrices are presented.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

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

    nlin.SI 2026-04 unverdicted novelty 7.0

    General theory for gauge equivalence and simplification of matrix Lax pairs in evolutionary differential-difference equations, applied to construct new two-component integrable systems and Miura transformations.