Bäcklund transformations for hyperbolic surfaces in $E^3$ via Weingarten congruences
Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 102-117 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

An investigation of the so-called Weingarten congruences in $E^3$ yields a system of partial differential equations (describing hyperbolic surfaces in $E^3$) and also its Bäcklund transformation.
@article{TMF_2000_122_1_a8,
     author = {M. Nieszporski and A. Sym},
     title = {B\"acklund transformations for hyperbolic surfaces in $E^3$ via {Weingarten} congruences},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {102--117},
     year = {2000},
     volume = {122},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a8/}
}
TY  - JOUR
AU  - M. Nieszporski
AU  - A. Sym
TI  - Bäcklund transformations for hyperbolic surfaces in $E^3$ via Weingarten congruences
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2000
SP  - 102
EP  - 117
VL  - 122
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a8/
LA  - ru
ID  - TMF_2000_122_1_a8
ER  - 
%0 Journal Article
%A M. Nieszporski
%A A. Sym
%T Bäcklund transformations for hyperbolic surfaces in $E^3$ via Weingarten congruences
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2000
%P 102-117
%V 122
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a8/
%G ru
%F TMF_2000_122_1_a8
M. Nieszporski; A. Sym. Bäcklund transformations for hyperbolic surfaces in $E^3$ via Weingarten congruences. Teoretičeskaâ i matematičeskaâ fizika, Tome 122 (2000) no. 1, pp. 102-117. http://geodesic.mathdoc.fr/item/TMF_2000_122_1_a8/

[1] B. Cenkl, Physica D, 18 (1986), 217–219 | DOI | MR | Zbl

[2] D. Levi, A. Sym, Phys. Lett. A, 149 (1990), 381–387 | DOI | MR

[3] S. P. Finikov, Teoriya kongruentsii, Gostekhizdat, M.–L., 1950

[4] M. Nieszporski, A. Sym, “Weingarten congruences and non-auto-Bäcklund transformations for hyperbolic surfaces”, Proc. of First Non-Orthodox School on Nonlinearity and Geometry, eds. D. Wójcik and J. Cieśliński, PWN, Warsaw, 1998, 37–40 | MR | Zbl

[5] R. Prus, A. Sym, “Rectilinear congruences and Bäcklund transformations: roots of the soliton theory”, Proc. of First Non-Orthodox School on Nonlinearity and Geometry, eds. D. Wójcik and J. Cieśliński, PWN, Warsaw, 1998, 25–36 | MR | Zbl

[6] J. Cieśliński, “Lie symmetries as a tool to isolate integrable geometries”, Nonlinear Evolution Equations and Dynamical Systems, eds. M. Boiti, L. Martina, and F. Pempinelli, World Scientific, Singapore, 1992, 260–268 | MR | Zbl

[7] H. Jonas, J. Deutsch. Math. Ver., 29 (1920), 40–74 | Zbl

[8] M. Lelieuvre, Bull. Sci. Math., 12 (1888), 126–128

[9] Th.-F. Moutard, J. Ec. Pol., 45 (1878), 1

[10] C. Athorne, Inverse Problems, 9 (1993), 217–232 | DOI | MR | Zbl

[11] V. B. Matveev, M. A. Sale, Darboux Transformations and Solitons, Springer-Verlag, Berlin, 1991 | MR

[12] C. Guichard, C. R. Acad. Sci. Paris, 110 (1890), 126–127; 112 (1891), 1424–1426

[13] A. Doliwa, P. M. Santini, Phys. Lett. A, 233 (1997), 365–372 | DOI | MR | Zbl

[14] L. Bianchi, Ann. Mat., 18:2 (1890), 301–358 | DOI | MR

[15] A. I. Bobenko, “Surfaces in terms of 2 by 2 matrices: Old and new integrable cases”, Harmonic Maps and Integrable Systems, Aspects of Math., E23, eds. A. P. Fordy and J. C. Wood, Braunschweig–Wiesbaden, 1994 | MR

[16] D. Korotkin, On some integrable cases in surface theory, Preprint Sfb 288 No116, Berlin, 1994 ; http://www-sfb288.math.tu-berlin.de | MR | Zbl

[17] J. Tafel, J. Geom. Phys., 17 (1995), 381–390 | DOI | MR | Zbl

[18] W. K. Schief, C. Rogers, M. E. Johnston, Chaos, Solitons, and Fractals, 5:1 (1995), 25–35 | DOI | MR

[19] W. K. Schief, Nonlinearity, 8 (1995), 1–9 | DOI | MR | Zbl

[20] J. Cieśliński, “The Darboux–Bianchi–Bäcklund transformation and soliton surfaces”, Proc. of First Non-Orthodox School on Nonlinearity and Geometry, eds. D. Wójcik and J. Cieśliński, PWN, Warsaw, 1998, 80–107 | MR