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arxiv: 0707.0575 · v1 · submitted 2007-07-04 · 🌊 nlin.SI

The Manakov system as two moving interacting curves

N. A. Kostov (Institute of Electronics , Bulgarian Academy of Sciences , Sofia , Bulgaria) , R. Dandoloff (Universit\'e de Cergy-Pontoise , Cergy-Pontoise , France) , V. S. Gerdjikov (Institute for Nuclear Research
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Nuclear Energy G. G. Grahovski (Institute for Nuclear Research
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keywords curvesinteractingmovingmanakovsystemappearsdenotingdensity
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The two time-dependent Schrodinger equations in a potential V(s,u), $u$ denoting time, can be interpreted geometrically as a moving interacting curves whose Fermi-Walker phase density is given by -dV/ds. The Manakov model appears as two moving interacting curves using extended da Rios system and two Hasimoto transformations.

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