ISSN:
1432-0916
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract: We apply a recently introduced [21, 15] reduction method, based on the ―∂ - dressing, to construct a large class of integrable reductions of the equations characterizing the multidimensional quadrilateral lattice (an N-dimensional lattice in ℝ M , N≤M, whose elementary quadrilaterals are planar and whose continuous limit describes submanifolds parametrized by conjugate lines [11]). We also show that, generically, in the limit of the small lattice parameter, half of these reductions lead to the Darboux equations for symmetric fields and the second half lead to the generalized Lamé equations describing N-dimensional submanifolds of ? M parametrized by conjugate orthogonal systems of coordinates. We finally show that a distinguished example of the second class of reductions corresponds to the multidimensional circular lattice (an N-dimensional lattice in ? M , N≤M, whose elementary quadrilaterals are inscribed in circles [7]).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s002200050411
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