Zobrazeno 1 - 10
of 182
pro vyhledávání: '"76m60"'
Autor:
Modin, Klas, Preston, Stephen C.
Zeitlin's model is a spatial discretization for the 2-D Euler equations on the flat 2-torus or the 2-sphere. Contrary to other discretizations, it preserves the underlying geometric structure, namely that the Euler equations describe Riemannian geode
Externí odkaz:
http://arxiv.org/abs/2408.11204
Autor:
Modin, Klas, Viviani, Milo
Two-dimensional (2-D) incompressible, inviscid fluids produce fascinating patterns of swirling motion. How and why the patterns emerge are long-standing questions, first addressed in the 19th century by Helmholtz, Kirchhoff, and Kelvin. Countless res
Externí odkaz:
http://arxiv.org/abs/2405.14282
Autor:
Kaptsov, E. I.
The study of the recently constructed group foliation for the geopotential forecast equation is continued. The group foliation consists of two systems, namely the automorphic and resolving systems, the analysis of which facilitates the derivation of
Externí odkaz:
http://arxiv.org/abs/2402.17663
Symmetry, which describes invariance, is an eternal concern in mathematics and physics, especially in the investigation of solutions to the partial differential equation (PDE). A PDE's nonlocally related PDE systems provide excellent approaches to se
Externí odkaz:
http://arxiv.org/abs/2401.14795
We obtain the optimal system's generating operators associated with the kind generalization of the Levinson Smith equation. Using those operators we characterize all invariant solutions associated with this equation. Moreover, we present the variatio
Externí odkaz:
http://arxiv.org/abs/2310.12438
Autor:
Constantineau, Kevin, García-Azpeitia, Carlos, García-Naranjo, Luis C, Lessard, Jean-Philippe
We consider the $N$-vortex problem on the sphere assuming that all vorticities have equal strength. We investigate relative equilibria (RE) consisting of $n$ latitudinal rings which are uniformly rotating about the vertical axis with angular velocity
Externí odkaz:
http://arxiv.org/abs/2309.04320
Autor:
Modin, Klas, Perrot, Manolis
Publikováno v:
Comm. Math. Phys., 405 (2024), 177
The two-dimensional (2-D) Euler equations of a perfect fluid possess a beautiful geometric description: they are reduced geodesic equations on the infinite-dimensional Lie group of symplectomorphims with respect to a right-invariant Riemannian metric
Externí odkaz:
http://arxiv.org/abs/2305.08479
Autor:
Ndogmo, J. C.
Publikováno v:
Appl. Math. Comput. 443 (2023) 127769
We apply an extension of a new method of group classification to a family of nonlinear wave equations labelled by two arbitrary functions, each depending on its own argument. The results obtained confirm the efficiency of the proposed method for grou
Externí odkaz:
http://arxiv.org/abs/2212.13238
We study the nonrigid dynamics induced by the standard birational actions of the split unitary groups $G=O_{o}\left( n,n\right) $, $SU\left( n,n\right) $ and $Sp\left( n,n\right) $ on the compact classical Lie groups $M=SO_{n}$, $% U_{n}$ and $Sp_{n}
Externí odkaz:
http://arxiv.org/abs/2203.03721
Autor:
Meleshko, Sergey V., Rogers, Colin
Publikováno v:
Open Communications in Nonlinear Mathematical Physics, Volume 1 (July 16, 2021) ocnmp:7358
Reciprocal transformations associated with admitted conservation laws were originally used to derive invariance properties in non-relativistic gasdynamics and applied to obtain reduction to tractable canonical forms. They have subsequently been shown
Externí odkaz:
http://arxiv.org/abs/2104.06078