Skip to main content
Log in

Perturbation Theory for Isotropic Landau-Lifschitz Equation Based on Inverse Scattering Transformation

  • Published:
International Journal of Theoretical Physics Aims and scope Submit manuscript

Abstract

The perturbation theory for the Landau-Lifschitz equation for isotropic chain with correction, which is based on the inverse scattering transform (IST), is developed to treat Landau-Lifschitz equation for a spin chain with axis asymmetry. The time-evolution equation of parameters and a formula for the first-order correction is given by treating the equation with axis symmetry as a perturbation to the isotropic equation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ao, S.-M. and Yan, J.-R. (2005). Journal of Physics A: General 38.

  • Borovik, A. E. (1978). JETP Letters 28, 629

    Google Scholar 

  • Bolovik, A. E. and Kulinich, S. I. (1984). JETP Letters 39, 320.

    Google Scholar 

  • Chen, X. J., Chen, Z. D., and Huang, N. N. (1998). Journal of Physics A 31, 6929.

    Article  MATH  MathSciNet  Google Scholar 

  • Dodd, R. K., Eilbeck, J. C., Gibbon, J. D., and Morris, H. D. (1982). Soliton and Nonlinear Wave Equation. Academic, New York.

    Google Scholar 

  • Faddeev, L. D. and Takhtajan, L. A. (1987). Hamiltonian Methods in the Theory of Solitons. Springer, Berlin.

    MATH  Google Scholar 

  • Feng-Ming, L., Hao, C., Zheng-you, L., Nian-Ning, H. (2004). Commun. Theory Physics (BeiJing, China) 41.

  • Fogedby, H. C. (1980). Journal of Physics A: Mathematical and General 13, 1467.

    Article  MathSciNet  ADS  Google Scholar 

  • Gerdjikov, V. S., Ivanov, M. I., and Kulish, P. P. (1980). TTheoretical and Mathematical Physics 44, 342.

    Google Scholar 

  • Hao, C. Nian-Ning, H. (2003). Chinese Physics Letters 20(4), 469.

    Article  ADS  Google Scholar 

  • Huang, N. N. (1996). Theory of Soliton and Method of Perturbations, ShangHai

  • Karpman, V. I. and Maslov, E. M. (1978). Perturbation theory for solitons. Sov. Physics JETP 46, 281–291

    MathSciNet  Google Scholar 

  • Karpman, V. I. (1979). Soliton evolution in the presence of perturbation. Physica Scripta 20, 462–478.

    MATH  MathSciNet  ADS  Google Scholar 

  • Kaup, D. J. and Newell, A. C. (1978a). Proceedings of Royal Society London, Series A 361, 413.

    ADS  Google Scholar 

  • Kaup, D. J. and Newell, A. C. (1978b). Journal of Mathematical Physics 19, 798.

    Article  MathSciNet  ADS  Google Scholar 

  • Kaup, D. J. and Newell, A. C. (1978c). Solitons as particles.osc illators, and in slowly changing media: a singular perturbation theory. Proceedings of Royal Society A 361, 413–446.

    ADS  Google Scholar 

  • Kivshar, Y. S. and Davies, B. L. (1998). Physics Reports 81, 298.

    Google Scholar 

  • Kivshar, Y. S. and Malomad, B. A. (1989). Dynamics of solitons in nearly integrable sestems. Reviews of Modern Physics 61. 763–915 and references therein.

    Article  ADS  Google Scholar 

  • Laksmanan, M. (1977). Physics Letters 61A, 53.

    ADS  Google Scholar 

  • Mjølhus, Z.E. (1989). Physica Scripta 40, 227.

    Article  ADS  Google Scholar 

  • Mjølhus, Z. E. and Hada, T. (1997). In Hada, T. and Matsumoto, H. eds., Nonlinear Waves and Chaos in Space Plasmas. Terrapub, Tokyo, p. 121.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Bai-Feng Yang.

Additional information

PACS numbers 05.45.Yv, 42.65.-k, 42.50.Md.

Supported by the National Science Foundation of China under Grant NO. 10474076 and No. 10375041.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, C., Yan, T., Cai, H. et al. Perturbation Theory for Isotropic Landau-Lifschitz Equation Based on Inverse Scattering Transformation. Int J Theor Phys 45, 2388–2395 (2006). https://doi.org/10.1007/s10773-006-9208-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10773-006-9208-y

Keywords

Navigation