Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates

Details Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates Exact soliton solutions and nonlinear modulation instability in spinor Bose-Einstein condensates

Sep 2005

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2005phrva..72c3611l&link_type=abstract

Physical Review A, vol. 72, Issue 3, id. 033611

Physics

61

Multicomponent Condensates, Spinor Condensates, Solitons, Exact Solutions

Scientific paper

We find one-, two-, and three-component solitons of the polar and ferromagnetic (FM) types in the general (nonintegrable) model of a spinor (three-component) model of the Bose-Einstein condensate, based on a system of three nonlinearly coupled Gross-Pitaevskii equations. The stability of the solitons is studied by means of direct simulations and, in a part, analytically, using linearized equations for small perturbations. Global stability of the solitons is considered by means of an energy comparison. As a result, ground-state and metastable soliton states of the FM and polar types are identified. For the special integrable version of the model, we develop the Darboux transformation (DT). As an application of the DT, analytical solutions are obtained that display full nonlinear evolution of the modulational instability of a continuous-wave state seeded by a small spatially periodic perturbation. Additionally, by dint of direct simulations, we demonstrate that solitons of both the polar and FM types, found in the integrable system, are structurally stable; i.e., they are robust under random changes of the relevant nonlinear coefficient in time.

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