Scattering of gap solitons by<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">PT</mml:mi></mml:math>-symmetric defects
Abstract
The resonant scattering of gap solitons (GSs) of the periodic nonlinear Schr\"odinger equation, with a localized defect which is symmetric under the parity and the time-reversal ($\mathcal{PT}$) symmetry, is investigated. It is shown that for suitable amplitudes ratios of the real and imaginary parts of the defect potential the resonant transmission of the GS through the defect becomes possible. The resonances occur for potential parameters which allow the existence of localized defect modes with the same energy and norm of the incoming GS. Scattering properties of gap solitons of different band gaps with effective masses of opposite sign are investigated. The possibility of unidirectional transmission and blockage of gap solitons by $\mathcal{PT}$ defect, as well as, amplification and destruction induced by multiple reflections from two $\mathcal{PT}$ defects, are also discussed.