A Nonlinear Schrödinger Equation Yielding the “Shape of Molecules” by Spontaneous Symmetry Breaking

1981 ◽  
pp. 255-266 ◽  
Author(s):  
Peter Pfeifer
Keyword(s):  
Schrödinger Equation ◽  
Symmetry Breaking ◽  
Spontaneous Symmetry Breaking ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger

scholarly journals Symmetry Breaking of PT-symmetric Solitons in Self-defocusing Saturable Nonlinear Schrödinger Equation

2021 ◽  
Author(s):  
Bo WenBo ◽  
Chao-Qing Dai ◽  
Yue-Yue Wang ◽  
Peng-Fei Li
Keyword(s):  
Schrödinger Equation ◽  
Symmetry Breaking ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Modulation Effect ◽  
Nonlinear Schrödinger ◽  
Power Threshold ◽  
The Stability ◽  
Power Region

Abstract The symmetry breaking phenomenon of the parity-time (PT) symmetric solitons in self-defocusing saturable nonlinear Schrödinger equation is studied. As the soliton power increases, branches of asymmetric solitons are separated from antisymmetric solitons, and they coexist with both symmetric and antisymmetric solitons. The anti-symmetric solitons require different power thresholds when they are under different saturable nonlinear strength. The stronger the saturable nonlinearity is, the larger the power threshold is. The saturable nonlinear strength has obvious modulation effect on the symmetry breaking of antisymmetric solitons and the bifurcation of the power curve. However, when the modulation strength of PT- symmetric potential increases, the effect of this modulation effect weakens. The antisymmetric solitons are only stable in the low power region, and the stability of symmetric and asymmetric solitons is less affected by the soliton power. The increase of the saturable nonlinear strength leads to the increase of the critical power of the symmetry breaking. When a beam propagates in a PT-symmetric optical waveguide, the symmetry breaking of antisymmetric solitons can be controlled by changing the saturable nonlinear strength.

A symmetry-breaking phenomenon and asymptotic profiles of least-energy solutions to a nonlinear Schrödinger equation

2005 ◽  
Vol 135 (2) ◽  
pp. 357-392 ◽  
Author(s):  
Kazuhiro Kurata ◽  
Tatsuya Watanabe ◽  
Masataka Shibata
Keyword(s):  
Schrödinger Equation ◽  
Symmetry Breaking ◽  
Nonlinear Schrödinger Equation ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
Nonlinear Schrödinger ◽  
Least Energy Solution ◽  
Image Position ◽  
Least Energy Solutions ◽  
Least Energy

In this paper, we study a symmetry-breaking phenomenon of a least-energy solution to a nonlinear Schrödinger equation under suitable assumptions on V(x), where λ > 1, p > 2 and χA is the characteristic function of the set A = [−(l + 2), −l] ∪ [l,l + 2] with l > 0. We also study asymptotic profiles of least-energy solutions for the singularly perturbed problem for small ε > 0.

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