Spontaneous Symmetry Breaking of Solitons Trapped in a Double-Gauss Potentials

Cuong Duy Nguyen, Khoa Xuan Dinh, Van Long Cao, Trippenbach M., Thuan Dinh Bui, Thuy Thanh Do


We consider an extended model of the model considered before with double-square potential, namely one-dimensional (1D) nonlinear Schrödinger equation (NLSE) with self-focusing nonlinearity and a 1D double-gauss potential. Spontaneous symmetry breaking has been presented in terms of the control parameter which is propagation constant in the case of optics and chemical potential in the of Bose-Einstein Condensate (BEC), correspondingly. The numerical simulations predict a bifurcation breaking the symmetry of 1D trapped in the double-gauss potential of the supercritical type as in the case of double-square potential. Furthermore we have constructed bifurcation diagrams considering the stability of solitons with three methods: the method using Vakhitov–Kolokolov (V-K) Stability Criterion, Pseudospectral Method and Method for Linear-Stability Eigenvalues. It will be shown that for our model the results obtained are the same for these three methods but the third one is the fastest.


Bose–Einstein condensate, nonlinear optical systems, double-square potential.

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DOI: https://doi.org/10.15625/0868-3166/28/4/13195 Display counter: Abstract : 277 views. PDF : 158 views.


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