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Two-field integrable evolutionary systems of the third order and their differential substitutions. (English) Zbl 1142.37045
Summary: 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.

##### MSC:
 37K10 Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) 35Q53 KdV equations (Korteweg-de Vries equations) 37K20 Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions
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