On the integrability of the inhomogeneous spherically symmetric Heisenberg ferromagnet in arbitrary dimensions

Daniel, M. ; Porsezian, K. ; Lakshmanan, M. (1994) On the integrability of the inhomogeneous spherically symmetric Heisenberg ferromagnet in arbitrary dimensions Journal of Mathematical Physics, 35 (12). pp. 6498-6510. ISSN 0022-2488

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Official URL: http://link.aip.org/link/?JMAPAQ/35/6498/1

Related URL: http://dx.doi.org/10.1063/1.530687

Abstract

The dynamics of an inhomogeneous spherically symmetric continuum Heisenberg ferromagnet in arbitrary (n-) dimensions is considered. By a known geometrical procedure the spin evolution equation equivalently is rewritten as a generalized nonlinear Schrodinger equation. A Painleve singularity structure analysis of the solutions of the equation shows that the system is integrable in arbitrary (n-) dimensions only when the inhomogeneity is of inverse power in the radial coordinate in the form f(r)=ε1r-2(n-1)2r-(n-2). This is confirmed by obtaining the associated Lax pair, Backlund transformation, and the solitonlike solution of the evolution equation. Further, calculations show that the one-dimensional linearly inhomogeneous ferromagnet acts as a universal model to which all the integrable higher-dimensional inhomogeneous spherically symmetric spin models can be formally mapped.

Item Type:Article
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ID Code:19352
Deposited On:22 Nov 2010 12:45
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