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Geometrical Description of the Local Integrals of Motion of Maxwell-Bloch Equation | A. V. Antonov
; A. A. Belov
; B. L. Feigin
; | Date: |
27 Dec 1994 | Journal: | Mod.Phys.Lett. A10 (1995) 1209-1224 | Subject: | hep-th | Abstract: | We represent a classical Maxwell-Bloch equation and related to it positive part of the AKNS hierarchy in geometrical terms. The Maxwell-Bloch evolution is given by an infinitesimal action of a nilpotent subalgebra $n_+$ of affine Lie algebra $hat {sl}_2$ on a Maxwell-Bloch phase space treated as a homogeneous space of $n_+$. A space of local integrals of motion is described using cohomology methods. We show that hamiltonian flows associated to the Maxwell-Bloch local integrals of motion (i.e. positive AKNS flows) are identified with an infinitesimal action of an abelian subalgebra of the nilpotent subalgebra $n_+$ on a Maxwell- Bloch phase space. Possibilities of quantization and latticization of Maxwell-Bloch equation are discussed. | Source: | arXiv, hep-th/9501128 | Services: | Forum | Review | PDF | Favorites |
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