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Transformations of quadrilateral lattices

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Doliwa, Adam y Santin, Maria Santin y Mañas Baena, Manuel (2000) Transformations of quadrilateral lattices. Journal of mathematical physics, 41 (2). pp. 944-990. ISSN 0022-2488

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URL Oficial: http://dx.doi.org/10.1063/1.533175


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Motivated by the classical studies on transformations of conjugate nets, we develop the general geometric theory of transformations of their discrete analogs: the multidimensional quadrilateral lattices, i.e., lattices x:Z(N)--> R-M, N less than or equal to M, whose elementary quadrilaterals are planar. Our investigation is based on the discrete analog of the theory of the rectilinear congruences, which we also present in detail. We study, in particular, the discrete analogs 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 <(partial derivative)over bar> formalism.


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©2000 American Institute of Physics.
A.D. would like to thank A. Sym for pointing out (see also Ref. 47) the important role of the rectilinear congruences in the theory of integrable geometries (soliton surfaces). He also acknowledges partial support from KBN Grant No. 2P03 B 18509. M.M. acknowledges partial support from CICYT Proyect No. PB95-0401 and from the exchange agreement between Università La Sapienza of Rome and Universidad Complutense of Madrid

Palabras clave:Integrable hierarchies; Coordinate systems; Hydrodynamic-type; Equation; Surfaces; Discretization
Materias:Ciencias > Física > Física-Modelos matemáticos
Ciencias > Física > Física matemática
Código ID:32473
Depositado:23 Jul 2015 10:32
Última Modificación:10 Dic 2018 15:10

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