78 citations · 1.2k across the 112 of their papers we have counts for
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Rotationally Symmetric Zoll Metrics with a Cubic Integral
Holger R. Dullin, Vladimir S. Matveev, Gleb P. Palshin +1
We introduce a new method for constructing Zoll metrics that admit first integrals polynomial in the momenta. The method uses Funk's form of the metric together with an algebraic r…
Thoughts about potentials with finite-band spectrum and finite-dimensional reductions of integrable systems
Andrey Yu. Konyaev, Vladimir S. Matveev
We repeat, using methods developed for BKM systems, the famous results of S. Novikov (1974), J. Moser (1981, 1982) , and A. Veselov (1980) that relate Schrödinger-Hill operators wi…
Finite-dimensional reductions and finite-gap type solutions of multicomponent integrable PDEs
Alexey V. Bolsinov, Andrey Yu. Konyaev, Vladimir S. Matveev
The main object of the paper is a recently discovered family of multicomponent integrable systems of partial differential equations, whose particular cases include many well-known…
Nonexistence of an integral of the 6th degree in momenta for the Zipoy-Voorhees metric
Boris S. Kruglikov, Vladimir S. Matveev
We prove nonexistence of a nontrivial integral that is polynomial in momenta of degree less than 7 for the Zipoy-Voorhees spacetime with the parameter
Two-dimensional superintegrable metrics with one linear and one cubic integral
Vladimir S. Matveev, Vsevolod V. Shevchishin
We describe all local Riemannian metrics on surfaces whose geodesic flows are superintegrable with one integral linear in momenta and one integral cubic in momenta. We also show th…
Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic flows admit integrals quadratic in momenta
Alexey V. Bolsinov, Vladimir S. Matveev, Giuseppe Pucacco
We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the geodesic flow admits a nontrivial integral quadratic in velocities. We construct local normal forms of…