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Rogue Wave Solutions for the Myrzakulov-I Equation

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Intelligent Mathematics II: Applied Mathematics and Approximation Theory

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 441))

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Abstract

In this paper, we consider the (2+1)-dimensional generalization of the Landau–Lifshitz equation, so-called the Myrzakulov-I (M-I) equation, which describes a two-dimensional dynamics of magnetization in ferromagnetics. The Darboux transformation (DT) for the M-I equation is constructed. Using the DT the solution of the type of destructive waves for the M-I equation is found.

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References

  1. Myrzakulov, R., Vijayalakshmi, S., Nugmanova, G., Lakshmanan, M.: A (2+1)-dimensional integrable spin model: geometrical and gauge equivalent counterpart, solitons and localized coherent structures. Phys. Lett. A 233, 391–396 (1997)

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  2. Myrzakulov, R., Nugmanova, G.N., Danlybaeva, A.K.: Geometry and multidimensional spliton equations. Theor. Math. Phys. 118(13), 441–451 (1999)

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  3. Myrzakulov, R., Nugmanova, G., Syzdykova, R.: Gauge equivalence between (2+1)-dimensional continuous Heisenberg ferromagnetic models and nonlinear Schr\(\dot{o}\)dinger-type equations. J. Phys. A: Math. Theor. 31(147), 9535–9545 (1998)

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  4. Zhang, Zh.-H., Deng, M., Zhao, W.-Zh., Ke, W.: On the integrable inhomogeneous Myrzakulov I equation. arXiv:nlin/0603069v1 [nlin.SI] 30 March 2006

  5. Chen, Ch., Zhou, Zi.-X.: Darboux transformation and exact solutions of the Myrzakulov I equation. Chin. Phys. Lett. 26(8), 080504 (2009)

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  6. Zhang, Y., Nie, X.-J., Zha, Q.-L.: Rogue wave solutions for the Heisenberg ferromagnet equations. Chin. Phys. Lett. 31(6), 060201 (2014)

    Article  Google Scholar 

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Authors and Affiliations

  1. L.N. Gumilyov Eurasian National University, Astana, Kazakhstan

    Gulgassyl Nugmanova

Authors
  1. Gulgassyl Nugmanova
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Correspondence to Gulgassyl Nugmanova .

Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, University of Memphis, Memphis, Tennessee, USA

    George A. Anastassiou

  2. Department of Mathematics, TOBB Economics and Technology University, Ankara, Turkey

    Oktay Duman

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Nugmanova, G. (2016). Rogue Wave Solutions for the Myrzakulov-I Equation. In: Anastassiou, G., Duman, O. (eds) Intelligent Mathematics II: Applied Mathematics and Approximation Theory. Advances in Intelligent Systems and Computing, vol 441. Springer, Cham. https://doi.org/10.1007/978-3-319-30322-2_8

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  • DOI: https://doi.org/10.1007/978-3-319-30322-2_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-30320-8

  • Online ISBN: 978-3-319-30322-2

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