dorsal/arxiv
View SchemaTransformations of Quadrilateral Lattices
| Authors | A. Doliwa, P. M. Santini, M. Manas |
|---|---|
| Categories | |
| ArXiv ID | solv-int/9712017 |
| URL | https://arxiv.org/abs/solv-int/9712017 |
| DOI | 10.1063/1.533175 |
| Journal | J. Math. Phys. 41 (2000) 944-990 |
Abstract
Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogues: the multidimensional quadrilateral lattices, i.e. lattices x: Z^N -> R^M, whose elementary quadrilaterals are planar. Our investigation is based on the discrete analogue of the theory of the rectilinear congruences, which we also present in detail. We study, in particular, the discrete analogues of the Laplace, Combescure, Levy, radial and fundamental transformations and their interrelations. The composition of these transformations and their permutability is also investigated from a geometric point of view. The deep connections between "transformations" and "discretizations" is also investigated for quadrilateral lattices. We finally interpret these results within the D-bar formalism.
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"abstract": "Motivated by the classical studies on transformations of conjugate nets, we\ndevelop the general geometric theory of transformations of their discrete\nanalogues: the multidimensional quadrilateral lattices, i.e. lattices x: Z^N -\u003e\nR^M, whose elementary quadrilaterals are planar. Our investigation is based on\nthe discrete analogue of the theory of the rectilinear congruences, which we\nalso present in detail. We study, in particular, the discrete analogues of the\nLaplace, Combescure, Levy, radial and fundamental transformations and their\ninterrelations. The composition of these transformations and their\npermutability is also investigated from a geometric point of view. The deep\nconnections between \"transformations\" and \"discretizations\" is also\ninvestigated for quadrilateral lattices. We finally interpret these results\nwithin the D-bar formalism.",
"arxiv_id": "solv-int/9712017",
"authors": [
"A. Doliwa",
"P. M. Santini",
"M. Manas"
],
"categories": [
"solv-int",
"nlin.SI"
],
"doi": "10.1063/1.533175",
"journal_ref": "J. Math. Phys. 41 (2000) 944-990",
"title": "Transformations of Quadrilateral Lattices",
"url": "https://arxiv.org/abs/solv-int/9712017"
},
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