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 and, Nuclear Energy, Bulgarian Academy of Sciences, Sofia, Bulgaria)
TL;DR
This paper interprets the Manakov system, a coupled Schrödinger equations model, as two interacting moving curves with a geometric phase related to the potential, linking integrable systems and differential geometry.
Contribution
It introduces a geometric interpretation of the Manakov system as two interacting curves using extended da Rios and Hasimoto transformations, connecting integrable PDEs with differential geometry.
Findings
Geometric interpretation of the Manakov system as interacting curves.
Relation between potential V(s,u) and Fermi-Walker phase density.
Extension of da Rios system to coupled curves.
Abstract
The two time-dependent Schrodinger equations in a potential V(s,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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Taxonomy
TopicsNonlinear Waves and Solitons · Nonlinear Photonic Systems · Quantum chaos and dynamical systems