Zobrazeno 1 - 10
of 56
pro vyhledávání: '"Marvan, Michal"'
Autor:
Marvan, Michal
We consider integrable curve nets in Euclidean space as a particular integrable geometry invariant with respect to rigid motions and net-preserving reparameterisations. For the purpose of their description, we first give an overview of the most impor
Externí odkaz:
http://arxiv.org/abs/2403.12626
Autor:
Marvan, Michal
Publikováno v:
J. Geom. Phys. 190 (2023) 104878
Addressing a long-standing problem, we show that every van Stockum dust can be matched to a 1-parametric family of non-static Papapetrou vacuum metrics, and the converse. The boundary, if existing, is determined by vanishing of certain first-order in
Externí odkaz:
http://arxiv.org/abs/2207.04740
Autor:
Marvan, Michal, Pavlov, Maxim V.
In this paper we construct multi-phase solutions for integrable dispersive chains associated with the three-dimensional linearly degenerate Mikhalev system of first order. These solutions are parameterized by infinitely many arbitrary parameters. As
Externí odkaz:
http://arxiv.org/abs/1802.10154
Autor:
Marvan, Michal, Pavlov, Maxim V.
We construct a point transformation between two integrable systems, the multi-component Harry Dym equation and the multi-component extended Harry Dym equation, that does not preserve the class of multi-phase solutions. As a consequence we obtain a ne
Externí odkaz:
http://arxiv.org/abs/1705.01792
Autor:
Hlaváč, Adam, Marvan, Michal
Publikováno v:
J. Geom. Phys. 113 (2017) 117-130
For the constant astigmatism equation, we construct a system of nonlocal conservation laws (an abelian covering) closed under the reciprocal transformations. We give functionally independent potentials modulo a Wronskian type relation.
Comment:
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Externí odkaz:
http://arxiv.org/abs/1602.06861
Autor:
Igonin, Sergei, Marvan, Michal
Publikováno v:
J. Geom. Phys. 85 (2014), 106--123
The Darboux-Egoroff system of PDEs with any number $n\ge 3$ of independent variables plays an essential role in the problems of describing $n$-dimensional flat diagonal metrics of Egoroff type and Frobenius manifolds. We construct a recursion operato
Externí odkaz:
http://arxiv.org/abs/1403.6109
Autor:
Hlaváč, Adam, Marvan, Michal
In this paper we continue investigation of the constant astigmatism equation z_{yy} + (1/z)_{xx} + 2 = 0. We newly interpret its solutions as describing spherical orthogonal equiareal patterns, with relevance to two-dimensional plasticity. We show ho
Externí odkaz:
http://arxiv.org/abs/1206.0321
Autor:
Hlaváč, Adam, Marvan, Michal
Publikováno v:
SIGMA 10 (2014), 091, 20 pages
We introduce a nonlocal transformation to generate exact solutions of the constant astigmatism equation $z_{yy} + (1/z)_{xx} + 2 = 0$. The transformation is related to the special case of the famous B\"acklund transformation of the sine-Gordon equati
Externí odkaz:
http://arxiv.org/abs/1111.2027
Autor:
Baran, Hynek, Marvan, Michal
Publikováno v:
J. Phys. A: Math. Theor. 42 (2009) 404007
Rediscovered by a systematic search, a forgotten class of integrable surfaces is shown to disprove the Finkel-Wu conjecture. The associated integrable nonlinear partial differential equation $$ z_{yy} + (1/z)_{xx} + 2 = 0 $$ possesses a zero curvatur
Externí odkaz:
http://arxiv.org/abs/1002.0989
Autor:
Baran, Hynek, Marvan, Michal
In this paper we classify Weingarten surfaces integrable in the sense of soliton theory. The criterion is that the associated Gauss equation possesses an sl(2)-valued zero curvature representation with a nonremovable parameter. Under certain restrict
Externí odkaz:
http://arxiv.org/abs/1002.0992