Zobrazeno 1 - 10
of 401
pro vyhledávání: '"Konyaev, P. A."'
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 Schr\"odinger-Hill operators with finite-band spectra, solutions of the Neumann system, and certain
Externí odkaz:
http://arxiv.org/abs/2411.02290
The paper surveys open problems and questions related to interplay between the theory of integrable systems with infinitely and finitely many degrees of freedom and Nijenhuis geometry. This text has grown out from preparatory materials for the series
Externí odkaz:
http://arxiv.org/abs/2410.04276
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 equations such as the Korteweg--de Vries, coupled KdV, Harry Dym, coup
Externí odkaz:
http://arxiv.org/abs/2410.00895
The core object of this paper is a pair $(L, e)$, where $L$ is a Nijenhuis operator and $e$ is a vector field satisfying a specific Lie derivative condition, i.e., $Lie_{e}L=\operatorname{Id}$. Our research unfolds in two parts. In the first part, we
Externí odkaz:
http://arxiv.org/abs/2311.04624
Publikováno v:
J. Geom. Phys. 195(2024), 105031
By a $(1,1)$-tensor field $K= K^i_j$, we construct an explicit system of differential invariants that vanish if and only if there (locally) exists a metric for which $K$ generates separation of variables.
Comment: 16 pages, no figures
Comment: 16 pages, no figures
Externí odkaz:
http://arxiv.org/abs/2307.15564
We describe all metrics geodesically compatible with a gl-regular Nijenhuis operator $L$. The set of such metrics is large enough so that a generic local curve $\gamma$ is a geodesic for a suitable metric $g$ from this set. Next, we show that a certa
Externí odkaz:
http://arxiv.org/abs/2306.13238
The paper contains two lines of results: the first one is a study of symmetries and conservation laws of gl-regular Nijenhuis operators. We prove the splitting Theorem for symmetries and conservation laws of Nijenhuis operators, show that the space o
Externí odkaz:
http://arxiv.org/abs/2304.10626
We construct all orthogonal separating coordinates in constant curvature spaces of arbitrary signature. Further, we construct explicit transformation between orthogonal separating and flat or generalised flat coordinates, as well as explicit formulas
Externí odkaz:
http://arxiv.org/abs/2212.01605
Publikováno v:
Dyn. Partial Differ. Equ. 20 (2023), no. 1, 73--98
We construct a new series of multicomponent integrable PDE systems that contain as particular example (with appropriately chosen parameters) many famous integrable systems including KdV, coupled KdV, Harry Dym, coupled Harry Dym, Camassa-Holm, multic
Externí odkaz:
http://arxiv.org/abs/2206.12942
Autor:
Anatoly S. Boreysho, Maxim A. Konyaev, Sergey Y. Strakhov, Andrey V. Trilis, Natalia V. Sotnikova
Publikováno v:
Sensors, Vol 24, Iss 21, p 6818 (2024)
This paper is devoted to the issue of using laser (lidar) sensing to determine wind speed and direction when solving practical problems during the analysis of meteorological conditions in the area around spaceports. This issue is relevant both for ma
Externí odkaz:
https://doaj.org/article/900347d8f3054efa962410b172ef4ca7
