Abstract
A new class of two-dimensional surfaces generated by formulas which are generalizations of the well known Lelieuvre and Schief formulas is presented. These surfaces are connected with two-dimensional spin systems which are stationary versions of the (2+1)-dimensional classical continuous Heisenberg ferromagnets.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Lakshmanan M. Phys. Lett. A, 61, 53 (1977)
Tsuchida T., Wadati M. J. Phys. Soc. Jpn., 68, 2241 (1999)
Rogers C., Schief W.K. Backlund and Darboux Transformations: Geometry and Modern Applications in Soliton Theory. London: Cambridge University Press, 2002.
Backlund and Darboux Transformations. The Geometry of Solitons. CRM Proceedings and Lecture Notes. V.29. Eds. A. Coley, D. Levi, R. Milson, C. Rogers, P. Winternitz. Aarms-Crm Workshop. American Mathematical Society, 2001.
Tenenblat K. Transformations of Manifolds and Application to Differential Equations. London: CRC Press, 1998.
Nonlinearity and Geometry. Eds. D. Wojcik, J. Cieslinski. Warszawa: Polish Scientific Publishers, 1998.
Cieslinski J., Goldstein P., Sym A. J. Phys. A: Math. Gen., 27, 1645 (1994)
Balakrishnan R., Guha P. J. Math. Phys., 37 3651 (1996)
Myrzakulov R.Integrability of the Gauss-Codazzi-Mainardi equation in 2+1 dimensions. In Progress in Nonlinear Science. Proc. of the Int. Conf. (Nizhny Novgorod, July 2–6, 2001). Mathematical Problems of Nonlinear Dynamics. V.I. Eds. L.M.Lerman, L.P.Shiľnikov. Nizhny Novgorod: University of Nizhny Novgorod, 2002. P.314–319.
Sym A. Soliton Surfaces and Their Applications: Soliton Geometry From Spectral Problems. Lect. Notes in Phys., 239, 154 (1985)
Doliwa A., Nieszporski M. J. Phys. A: Math. Gen., 34, 10423 (2001)
Schief W.K. J. Math. Phys., 41, 6566 (2000)
Myrzakulov R., Vijayalakshmi S., Syzdykova R.N., Lakshmanan M. J. Math. Phys., 39, 2122 (1998)
Lakshmanan M., Vijayalakshmi S., Danlybaeva A.K., Myrzakulov R. J. Math. Phys., 39, 3765 (1998)
Lakshmanan M. Geometrical interpretation of (2+1)-dimensional integrable nonlinear evolution equations and localized solutions. Mathematisches Forschungsinstitut Oberwolfach. Report/40/97. ps, p.9.
Gutshabash E.Sh. Some notes on Ishimori’s magnet model. E-preprint: nlin.SI/0302002
Estevez P.G., Hernaez G.A. Lax pair, Darboux Transformations and solitonic solutions for a (2+1)-dimensional nonlinear Schrodinger equation. E-preprint: solv-int/9910005
Chou K.S., Qu C.Z. J. Phys. Soc. Jpn., 71, 1039 (2002)
Konopelchenko B.G. Stud. Appl. Math., 96, 9 (1996)
Konopelchenko B.G., Pinkall U. Geometriae Dedicata, 6, 11 (1999)
Ferapontov E.V. Surfaces with flat normal bundle: an explicit construction. E-preprint: math.DG/9805012
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Kluwer Academic Publishers
About this paper
Cite this paper
Rahimov, F.K., Myrzakul, K., Serikbaev, N.S., Myrzakulov, R. (2004). On the Geometry of Stationary Heisenberg Ferromagnets. In: Abdullaev, F.K., Konotop, V.V. (eds) Nonlinear Waves: Classical and Quantum Aspects. NATO Science Series II: Mathematics, Physics and Chemistry, vol 153. Springer, Dordrecht. https://doi.org/10.1007/1-4020-2190-9_46
Download citation
DOI: https://doi.org/10.1007/1-4020-2190-9_46
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-2188-6
Online ISBN: 978-1-4020-2190-9
eBook Packages: Chemistry and Materials ScienceChemistry and Material Science (R0)