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15 papers · 1 filter
Multidimensional integrable systems from contact geometry
A. Sergyeyev
Upon having presented a bird's eye view of history of integrable systems, we give a brief review of certain earlier advances (arXiv:1401.2122 & arXiv:1812.02263) in the longstandin…
Point- and contact-symmetry pseudogroups of dispersionless Nizhnik equation
Vyacheslav M. Boyko, Roman O. Popovych, Oleksandra O. Vinnichenko
Applying an original megaideal-based version of the algebraic method, we compute the point-symmetry pseudogroup of the dispersionless (potential symmetric) Nizhnik equation. This i…
Integrable (3+1)-dimensional system with an algebraic Lax pair
A. Sergyeyev
We present a first example of an integrable (3+1)-dimensional dispersionless system with nonisospectral Lax pair involving algebraic, rather than rational, dependence on the spectr…
Integrability of anti-self-dual vacuum Einstein equations with nonzero cosmological constant: an infinite hierarchy of nonlocal conservation laws
I. Krasil'shchik, A. Sergyeyev
We present an infinite hierarchy of nonlocal conservation laws for the Przanowski equation, an integrable second-order PDE locally equivalent to anti-self-dual vacuum Einstein equa…
Reductions of the universal hierarchy and rdDym equations and their symmetry properties
P. Holba, I. S. Krasil'shchik, O. I. Morozov +1
We consider the equations and that arise as reductions of the universal hierarchy and…
Symmetry reductions and exact solutions of Lax integrable -dimensional systems
H. Baran, I. S. Krasil'shchik, O. I. Morozov +1
We present a complete description of -dimensional equations that arise as symmetry reductions of fourf -dimensional Lax-integrable equations: (1) the universal hierarchy equa…