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TMF, 1999, Volume 118, Number 3, Pages 441–451 (Mi tmf717)  

This article is cited in 14 scientific papers (total in 14 papers)

Geometry and multidimensional soliton equations

R. Myrzakulov, A. K. Danlybaeva, G. N. Nugmanova

Institute of Physics and Technology, Ministry of Education and Science of the Republic of Kazakhstan

Abstract: The connection between the differential geometry of curves and $(2+1)$-dimensional integrable systems is established. The Zakharov equation, the modified Veselov–Novikov equation, the modified Korteweg–de Vries equation, etc., are equivalent in the Lakshmanan sense to $(2+1)$-dimensional spin systems.


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English version:
Theoretical and Mathematical Physics, 1999, 118:3, 347–356

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Citation: R. Myrzakulov, A. K. Danlybaeva, G. N. Nugmanova, “Geometry and multidimensional soliton equations”, TMF, 118:3 (1999), 441–451; Theoret. and Math. Phys., 118:3 (1999), 347–356

Citation in format AMSBIB
\by R.~Myrzakulov, A.~K.~Danlybaeva, G.~N.~Nugmanova
\paper Geometry and multidimensional soliton equations
\jour TMF
\yr 1999
\vol 118
\issue 3
\pages 441--451
\jour Theoret. and Math. Phys.
\yr 1999
\vol 118
\issue 3
\pages 347--356

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    This publication is cited in the following articles:
    1. Martina, L, “Deformation of surfaces, integrable systems, and Chern–Simons theory”, Journal of Mathematical Physics, 42:3 (2001), 1397  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    2. Serikbaev N.S., Myrzakul K., Rahimov F.K., Myrzakulov R., “On Continuous Limits of Some Generalized Compressible Heisenberg Spin Chains”, Nonlinear Waves: Classical and Quantum Aspects, Nato Science Series II Mathematics Physics and Chemistry, 153, 2005, 535–542  crossref  mathscinet  adsnasa  isi
    3. Anco S.C., Myrzakulov R., “Integrable generalizations of Schrodinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces”, J Geom Phys, 60:10 (2010), 1576–1603  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    4. Myrzakulov R., Mamyrbekova G.K., Nugmanova G.N., Yesmakhanova K.R., Lakshmanan M., “Integrable Motion of Curves in Self-Consistent Potentials: Relation To Spin Systems and Soliton Equations”, Phys. Lett. A, 378:30-31 (2014), 2118–2123  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus  scopus
    5. Myrzakulov R., Mamyrbekova G., Nugmanova G., Lakshmanan M., “Integrable (2+1)-Dimensional Spin Models With Self-Consistent Potentials”, Symmetry-Basel, 7:3 (2015), 1352–1375  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    6. Yersultanova Z.S., Zhassybayeva M., Yesmakhanova K., Nugmanova G., Myrzakulov R., “Darboux Transformation and Exact Solutions of the Integrable Heisenberg Ferromagnetic Equation With Self-Consistent Potentials”, Int. J. Geom. Methods Mod. Phys., 13:1 (2016), 1550134  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    7. Yan Zh., Gegenhasi, “On a integrable deformations of Heisenberg supermagnetic model”, J. Nonlinear Math. Phys., 23:3 (2016), 335–342  crossref  mathscinet  isi  elib  scopus
    8. Nugmanova G., “Rogue Wave Solutions for the Myrzakulov-I Equation”, Intelligent Mathematics II: Applied Mathematics and Approximation Theory, Advances in Intelligent Systems and Computing, 441, eds. Anastassiou G., Duman O., Springer-Verlag Berlin, 2016, 119–125  crossref  mathscinet  isi  scopus
    9. Yesmahanova K.R., Shaikhova G.N., Bekova G.T., Myrzakulova Zh.R., “Determinant Reprentation of Dardoux Transformation for the (2+1)-Dimensional Schr?dinger-Maxwell-Bloch Equation”, Intelligent Mathematics II: Applied Mathematics and Approximation Theory, Advances in Intelligent Systems and Computing, 441, eds. Anastassiou G., Duman O., Springer-Verlag Berlin, 2016, 183–198  crossref  isi  scopus
    10. Yesmakhanova K., Bekova G., Shaikhova G., Myrzakulov R., “Soliton Solutions of the (2+1)-Dimensional Complex Modified Korteweg-de Vries and Maxwell-Bloch Equations”, 5Th International Conference on Mathematical Modeling in Physical Sciences (Ic-Msquare 2016), Journal of Physics Conference Series, 738, eds. Vagenas E., Vlachos D., IOP Publishing Ltd, 2016, UNSP 012018  crossref  isi  scopus  scopus  scopus
    11. Nugmanova G.N., Sagidullayeva Zh.M., “Generalized Spin Model With Vector Potential and Its Solution”, Bull. Karaganda Univ-Math., 86:2 (2017), 91–96  isi
    12. Myrzakul A., Myrzakulov R., “Integrable Geometric Flows of Interacting Curves/Surfaces, Multilayer Spin Systems and the Vector Nonlinear Schrodinger Equation”, Int. J. Geom. Methods Mod. Phys., 14:10 (2017), 1750136  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    13. Myrzakul A., Myrzakulov R., “Integrable Motion of Two Interacting Curves, Spin Systems and the Manakov System”, Int. J. Geom. Methods Mod. Phys., 14:7 (2017), 1750115  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    14. Nugmanova G., Sagidullayeva Zh., Myrzakulov R., “Hirota'S Method For a Spin Model With Self-Consistent Potential”, Xxiv International Conference on Integrable Systems and Quantum Symmetries (Isqs-24), Journal of Physics Conference Series, 804, IOP Publishing Ltd, 2017, UNSP 012035  crossref  isi  scopus  scopus
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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