The symmetric, D-invariant and Egorov reductions of the quadrilateral lattice

Doliwa, Adam; Santini, P.

doi:10.1016/s0393-0440(00)00011-5

Cited by 57 publications

(123 citation statements)

References 32 publications

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“…In Ref. 18 the symmetric and Egorov lattices were introduced-the Egorov lattice was also introduced by Schief. The symmetric lattice appears when backward and forward data of the lattice are related in a particular way.…”

Section: Reduced Latticesmentioning

confidence: 99%

“…ᮀ This is the backward representation of the quadrilateral lattice as explained in Ref. 18. Moreover, the functions i introduced there can be identified with…”

Section: Definition 3: Discrete Backward Rotation Coefficients and Lamentioning

confidence: 99%

“…18, for pϭN and qϭ0 ͑the Euclidean case͒ the corresponding quadrilateral lattice is circular. Thus, we are dealing with extensions of the circular lattice to pseudoEuclidean spaces.…”

Section: ͑53͒mentioning

confidence: 99%

“…In Sec. III we generate quadrilateral lattices and give their geometrical elements, including those of the backward lattice, 18 in terms of the Cauchy propagator. Section IV is devoted to the generation, by means of singular dressing, of the a͒ Electronic mail: manuel@darboux.fis.ucm.es and http://darboux.fis.ucm.es reduced lattices.…”

Section: Introductionmentioning

confidence: 99%

“…[20][21][22] We finally characterize the discrete fundamental transformations for the symmetric lattices of Ref. 18.…”

Section: Introductionmentioning

confidence: 99%

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From integrable nets to integrable lattices

Mañas

2002

Journal of Mathematical Physics

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Inspired by the results of Jonas, Einsenhart, Demoulin, and Bianchi on the permutability property of classical geometrical transformations of conjugate nets and its reductions-of pseudo-orthogonal, pseudo-symmetric, and pseudo-Egorov typesdressing transformations of the N-component KP hierarchy ͑described within the Grassmannian͒ are used to generate quadrilateral lattices and its corresponding reductions. As a byproduct we get the corresponding discrete dressing transformations; in particular, we characterize the vectorial fundamental discrete transformations preserving the symmetric lattice.

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Section: Reduced Latticesmentioning

confidence: 99%

“…ᮀ This is the backward representation of the quadrilateral lattice as explained in Ref. 18. Moreover, the functions i introduced there can be identified with…”

Section: Definition 3: Discrete Backward Rotation Coefficients and Lamentioning

confidence: 99%

“…18, for pϭN and qϭ0 ͑the Euclidean case͒ the corresponding quadrilateral lattice is circular. Thus, we are dealing with extensions of the circular lattice to pseudoEuclidean spaces.…”

Section: ͑53͒mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…[20][21][22] We finally characterize the discrete fundamental transformations for the symmetric lattices of Ref. 18.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations