Energy transport in an inhomogeneous Heisenberg ferromagnetic chain
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.
KeywordsContinuum Limit Soliton Solution Energy Transport Nonlinear Evolution Equation Twisted Space
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- M. Lakshmanan, Continuum spin systems as an exactly solvable dynamical system. Phys. Lett. 61A,, 53–54 (1972).Google Scholar
- 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
- R. Balakrishnan, On the inhomogeneous Heisenberg chain. J. Phys. C15, L1305–L1308 (1982).Google Scholar
- 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
- 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
- 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
- R. Balakrishnan, Dynamics of a generalized classical Heisenberg chain. Phys. Lett. 92A,, 243–246 (1982).Google Scholar
- 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
- L. A. Takhtajan, Integration of the continuous Heisenberg spin chain through the inverse scattering method. Phys. Lett. 64A, 235–237 (1977).Google Scholar