Energy transport in an inhomogeneous Heisenberg ferromagnetic chain

  • Radha Balakrishnan
Part of the Lecture Notes in Physics book series (LNP, volume 189)


The spin evolution equation of a classical inhomogeneous Heisenberg chain is derived and its exact equivalence (in the continuum limit) to a generalized nonlinear Schrödinger equation with x-dependent coefficients is proved. An extension of the AKNS-ZS formalism is given which enables us to solve the latter equation exactly for certain specific inhomogeneities. Energy-momentum transport along the chain is related to the solution of this equation.


Continuum Limit Soliton Solution Energy Transport Nonlinear Evolution Equation Twisted Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Lakshmanan, Continuum spin systems as an exactly solvable dynamical system. Phys. Lett. 61A,, 53–54 (1972).Google Scholar
  2. [2]
    V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulating waves in nonlinear media. Sov. Phys. JETP 34, 62–69 (1972).Google Scholar
  3. [3]
    G. S. Gardner, M. D. Kruskal, R. M. Miura, and J. M. Greene, Method of solving the Korteweg-de Vries equation. Phys. Rev. Lett. 19, 1095–1097 (1967).CrossRefGoogle Scholar
  4. [4]
    G. L. Lamb, Jr., Solitons on moving space curves. J. Math. Phys. 18, 1654–1661 (1977).CrossRefGoogle Scholar
  5. [5]
    R. Balakrishnan, On the inhomogeneous Heisenberg chain. J. Phys. C15, L1305–L1308 (1982).Google Scholar
  6. [6]
    F. Calogero and A. Degasperis, Exact solution via the spectral transform of a generalization with linearly x-dependent coefficients of the nonlinear Schrödinger equation. Lett. Nuovo Cimento 22, 420–424 (1978).Google Scholar
  7. [7]
    M. Lakshamanan and R. K. Bullough, Geometry of generalized nonlinear Schrödinger and Heisenberg ferromagnetic spin equations with linearly -dependent coefficients. Phys. Lett. 80A,, 287–292 (1980).Google Scholar
  8. [8]
    M. J. Ablowitz, D. J. Kaup, A. C. Newell, and H. Segur, The inverse scattering transform analysis for nonlinear problems. Stud. Appl. Math. 53, 249–315 (1974).Google Scholar
  9. [9]
    R. Balakrishnan, Dynamics of a generalized classical Heisenberg chain. Phys. Lett. 92A,, 243–246 (1982).Google Scholar
  10. [10]
    M. R. Gupta, Exact inverse scattering solution of a nonlinear evolution equation in a non-uniform medium. Phys. Lett. 72A,, 420–422 (1979).Google Scholar
  11. [11]
    L. A. Takhtajan, Integration of the continuous Heisenberg spin chain through the inverse scattering method. Phys. Lett. 64A, 235–237 (1977).Google Scholar

Copyright information

© Springer-Verlag 1983

Authors and Affiliations

  • Radha Balakrishnan
    • 1
  1. 1.Department of Theoretical PhysicsUniversity of MadrasIndia

Personalised recommendations