Interactions of bright and dark solitons with localized $\mathcal{P}\mathcal{T}$-symmetric potentials

Abstract

We study collisions of moving nonlinear-Schrödinger solitons with a $\mathcal{P}\mathcal{T}$-symmetric dipole embedded into the one-dimensional self-focusing or defocusing medium. Accurate analytical results are produced for bright solitons, and, in a more qualitative form, for dark ones. In the former case, an essential aspect of the approximation is that it must take into regard the intrinsic chirp of the soliton, thus going beyond the framework of the simplest quasi-particle description of the soliton's dynamics. Critical velocities separating reflection and transmission of the incident bright solitons are found by means of numerical simulations, and in the approximate semi-analytical form. An exact solution for the dark soliton pinned by the complex $\mathcal{P}\mathcal{T}$-symmetric dipole is produced too.

12 pages, 5 figures

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Cited by in corpus (7)

• Nonlinear waves in $\mathcal{P}\mathcal{T}$-symmetric systems
• Nonlinear switching and solitons in PT-symmetric photonic systems
• Discrete solitons in self-defocusing systems with $\mathcal{P}\mathcal{T}$-symmetric defects
• Attraction centers and PT-symmetric delta-functional dipoles in critical and supercritical self-focusing media
• Fundamental and vortex dissipative quadratic solitons supported by spatially localized gain
• Stability analysis and attractor dynamics of 3D dark solitons with localized dissipation
• Unidirectional segregation of Bright-Bright soliton through a $\mathcal{P}\mathcal{T}$-symmetric potential