Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Bolsinov, A. V."'
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
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
Publikováno v:
J. Geom. Anal. 33 (2023), no. 6, 193
We consider multicomponent local Poisson structures of the form $\mathcal P_3 + \mathcal P_1$, under the assumption that the third order term $\mathcal P_3$ is Darboux-Poisson and non-degenerate, and study the Poisson compatibility of two such struct
Externí odkaz:
http://arxiv.org/abs/2112.09471
Publikováno v:
Nonlinearity 34 (8)(2021): 5136--5162
We connect two a priori unrelated topics, theory of geodesically equivalent metrics in differential geometry, and theory of compatible infinite dimensional Poisson brackets of hydrodynamic type in mathematical physics. Namely, we prove that a pair of
Externí odkaz:
http://arxiv.org/abs/2009.07802
Publikováno v:
European Journal of Mathematics (2021)
We study and completely describe pairs of compatible Poisson structures near singular points of the recursion operator satisfying natural non-degeneracy condition.
Externí odkaz:
http://arxiv.org/abs/2001.04851