TY - JOUR AU - Nguyen, Cuong Duy AU - Dinh, Khoa Xuan AU - Cao, Van Long AU - M., Trippenbach AU - Bui, Thuan Dinh AU - Do, Thuy Thanh PY - 2018/12/27 Y2 - 2024/03/29 TI - Spontaneous Symmetry Breaking of Solitons Trapped in a Double-Gauss Potentials JF - Communications in Physics JA - Comm. Phys. VL - 28 IS - 4 SE - Papers DO - 10.15625/0868-3166/28/4/13195 UR - https://vjs.ac.vn/index.php/cip/article/view/13195 SP - 301 AB - 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. ER -