TY - JOUR

T1 - Trapped states and transitions between them in double-well pseudopotentials

AU - Mayteevarunyoo, T.

AU - Malomed, B. A.

AU - Dong, G.

N1 - Funding Information:
ACKNOWLEDGMENTS The work of T.M. was supported, in a part, by a postdoctoral fellowship from the Pikovsky–Valazzi Foundation, by the Israel Science Foundation through the Center-of-Excellence grant no. 8006/03, and by the Thailand Research Fund under grant no. MRG5080171.

PY - 2009/4

Y1 - 2009/4

N2 - We analyze a model of a double-well pseudopotential (DWPP), based in the 1D Gross-Pitaevskii equation with a spatially modulated self-attractive nonlinearity. In the limit case when the DWPP structure reduces to the local nonlinearity coefficient represented by a set of two delta-functions, analytical solutions are obtained for symmetric, antisymmetric and asymmetric states. In this case, the transition from symmetric to asymmetric states, i.e., a spontaneous-symmetry-breaking (SSB) bifurcation, is subcritical. Numerical analysis demonstrates that the symmetric states are stable up to the SSB point, while emerging asymmetric states (together with all antisymmetric solutions) are unstable in the delta-function model. In a general model, which features a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the bifurcation into the supercritical type. Antisymmetric solutions may also enjoy stabilization in the finite-width DWPP structure, demonstrating a bistability involving the asymmetric states. The symmetric states require a finite norm for their existence. A full diagram for the existence and stability of the trapped states is produced for the general model.

AB - We analyze a model of a double-well pseudopotential (DWPP), based in the 1D Gross-Pitaevskii equation with a spatially modulated self-attractive nonlinearity. In the limit case when the DWPP structure reduces to the local nonlinearity coefficient represented by a set of two delta-functions, analytical solutions are obtained for symmetric, antisymmetric and asymmetric states. In this case, the transition from symmetric to asymmetric states, i.e., a spontaneous-symmetry-breaking (SSB) bifurcation, is subcritical. Numerical analysis demonstrates that the symmetric states are stable up to the SSB point, while emerging asymmetric states (together with all antisymmetric solutions) are unstable in the delta-function model. In a general model, which features a finite width of the nonlinear-potential wells, the asymmetric states quickly become stable, simultaneously with the switch of the bifurcation into the supercritical type. Antisymmetric solutions may also enjoy stabilization in the finite-width DWPP structure, demonstrating a bistability involving the asymmetric states. The symmetric states require a finite norm for their existence. A full diagram for the existence and stability of the trapped states is produced for the general model.

UR - http://www.scopus.com/inward/record.url?scp=65249186385&partnerID=8YFLogxK

U2 - 10.1134/S1054660X09040124

DO - 10.1134/S1054660X09040124

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AN - SCOPUS:65249186385

SN - 1054-660X

VL - 19

SP - 602

EP - 609

JO - Laser Physics

JF - Laser Physics

IS - 4

ER -