The numerical simulations predict a bifurcation breaking the symmetry of 1D solitons 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 including the method using Vakhitov–Kolokolov (V-K) Stability Criterion, Pseudospectral Method and Method for Linear-Stability Eigenvalues. It will show that the obtained results of our model from the three methods are the same but the third one is the fastest. | Communications in Physics, Vol. 28, No. 4 (2018), pp. 301-310 DOI: SPONTANEOUS SYMMETRY BREAKING OF SOLITONS TRAPPED IN A DOUBLE-GAUSS POTENTIAL NGUYEN DUY CUONG1,2,† , DINH XUAN KHOA1 , CAO LONG VAN3 , M. TRIPPENBACH4,5 , BUI DINH THUAN1 , AND DO THANH THUY1 1 Vinh University, 182 Le Duan Street, Vinh City, Vietnam 2 Industrial University of Vinh, 26 Nguyen Thai Hoc Street, Vinh City, Vietnam 3 University of Zielona G´ ora, ul. Licealna 9, 65-417 Zielona G´ora, Poland 4 Institute of Theoretical Physics, Physics Department, Warsaw University, Hoza 69, PL-00-681 Warsaw, Poland 5 Soltan Institute for Nuclear Studies, Ho˙za 69, PL-00-681 Warsaw, Poland † E-mail: duycuonghui@ Received 16 October 2018 Accepted for publication 29 November 2018 Published 15 December 2018 Abstract. We consider an extended model of the previously considered model with double-square potential which is namely one-dimensional (1D) nonlinear Schr¨odinger 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 case of Bose-Einstein Condensate (BEC), correspondingly. The numerical simulations predict a bifurcation breaking the symmetry of 1D solitons 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 including the method using Vakhitov–Kolokolov (V-K) Stability Criterion, Pseudospectral Method and Method for Linear-Stability Eigenvalues. It will show that the obtained results of our model from the three methods are the same but the third one is the fastest. Keywords: Bose–Einstein condensate, nonlinear optical systems, double-square potential. Classification numbers: . c 2018 Vietnam Academy of
