On a discretization of asymptotic nets
| Autor: | Maciej Nieszporski |
|---|---|
| Rok vydání: | 2002 |
| Předmět: |
Asymptotic analysis
Quadrilateral Dynamical systems theory Discretization Integrable system General Physics and Astronomy Discrete geometry Algebra Nonlinear system Nonlinear Sciences::Exactly Solvable and Integrable Systems Applied mathematics Geometry and Topology Mathematical Physics Differential (mathematics) Mathematics |
| Zdroj: | Journal of Geometry and Physics. 40:259-276 |
| ISSN: | 0393-0440 |
| DOI: | 10.1016/s0393-0440(01)00038-9 |
| Popis: | We discretize some notions of the theory of asymptotic nets and of the theory of transformations of asymptotic nets. These are the Lelieuvre formulas, the Moutard equation, the Moutard transformation, the Weingarten congruences and the Jonas formulas. It allows us to extend the theory of reductions of the discrete version of the Darboux system, applied primarily to multidimensional quadrilateral lattices, on the theory of discrete asymptotic nets which in turn is helpful in a discretization of some classical differential nonlinear integrable systems of physical interest, e.g. the Ernst equation and the stationary modified Nizhnik–Veselov–Novikov system (in form which we call the Fubini–Ragazzi system). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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