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تسجيل مستخدم جديدNonlinear PT-symmetric models bearing exact solutions
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We study the nonlinear Schr$ddot{o}$dinger equation with a PT-symmetric potential. Using a hydrodynamic formulation and connecting the phase gradient to the field amplitude, allows for a reduction of the model to a Duffing or a generalized Duffing equation. This way, we can obtain exact soliton solutions existing in the presence of suitable PT-symmetric potentials, and study their stability and dynamics. We report interesting new features, including oscillatory instabilities of solitons and (nonlinear) PT-symmetry breaking transitions, for focusing and defocusing nonlinearities.
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We explore the consequences of incorporating parity and time reversal ($mathcal{PT}$) symmetries on the dynamics of nonreciprocal light propagation exhibited by a class of nonuniform periodic structures known as chirped $mathcal{PT}$-symmetric fiber
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the systems undergo significant changes. On an example of an array of four waveguides described by the discrete nonlinear Schrodinger equation with dissipation and gain, we show that the equivalence of the underlying linear spectra implies similarity of neither structure nor stability of the nonlinear modes in the arrays. Even the existence of one-parametric families of nonlinear modes is not guaranteed by the PT symmetry of a newly obtained system. Neither the stability is directly related to the PT symmetry: stable nonlinear modes exist even when the spectrum of the linear array is not purely real. We use graph representation of PT-symmetric networks allowing for simple illustration of linearly equivalent networks and indicating on their possible experimental design.
The subject of PT-symmetry and its areas of application have been blossoming over the past decade. Here, we consider a nonlinear Schrodinger model with a complex potential that can be tuned controllably away from being PT-symmetric, as it might be th
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