Integrability properties of the four-dimensional equation of the universal hierarchy

O. I. Morozov

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference "Geometric Methods in Control Theory and Mathematical Physics" dedicated to the 70th anniversary of S.L. Atanasyan, the 70th anniversary of I.S. Krasilshchik, the 70th anniversary of A.V. Samokhin, and the 80th anniversary of V.T. Fomenko. S.A. Esenin Ryazan State University, Ryazan, September 25–28, 2018. Part 2, Tome 169 (2019), pp. 48-55.

Résumé

Properties associated with the integrability of the four-dimensional equation of the universal hierarchy are considered. In particular, the structure of the algebra of its local symmetries is studied. We show that the second group of exotic cohomologies of this algebra is nontrivial. We prove that the spectral parameter in the well-known covering of this equation is irremovable. A shadow of nonlocal symmetry was found; using it, we construct the recursion operator. The action of the recursion operator on some local symmetries generates new non-Abelian coverings of the equation.

Détail

Keywords: integrable differential equation, differential covering, symmetry, recursion operator.

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