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

doi:10.15625/0868-3166/28/4/13195

Author affiliations

Authors

Cuong Duy Nguyen (1) Vinh University, 182 Le Duan Street, Vinh City, Vietnam. (2) Industrial University of Vinh, 26 Nguyen Thai Hoc Street, Vinh City, Vietnam. https://orcid.org/0000-0002-1395-1249
Khoa Xuan Dinh Vinh University, 182 Le Duan Street, Vinh City, Vietnam
Van Long Cao University of Zielona Góra, ul. Licealna 9, 65-417 Zielona Góra, Poland
Trippenbach M. Institute of Theoretical Physics, Physics Department, Warsaw University, Hoża 69, PL-00-681 Warsaw, Poland. and Soltan Institute for Nuclear Studies, Hoża 69, PL-00-681 Warsaw, Poland.
Thuan Dinh Bui Vinh University, 182 Le Duan Street, Vinh City, Vietnam
Thuy Thanh Do

DOI:

https://doi.org/10.15625/0868-3166/28/4/13195

Keywords:

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

Abstract

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.

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