F. Kh. Abdullaev, V.A. Brazhnyi, M. Salerno
The resonant scattering of gap solitons (GS) of the periodic nonlinear Schr\”odinger equation with a localized defect which is symmetric under the parity and the time-reversal (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 GSs of different band-gaps with effective masses of opposite sign are investigated. The possibility of unidirectional transmission and blockage of GSs by PT defect, as well as, amplification and destruction induced by multiple reflections from two PT defects, are also discussed.
http://arxiv.org/abs/1309.7655
Pattern Formation and Solitons (nlin.PS); Quantum Gases (cond-mat.quant-gas); Atomic Physics (physics.atom-ph); Optics (physics.optics)
A.S. Rodrigues, K. Li, V. Achilleos, P.G. Kevrekidis, D.J. Frantzeskakis, Carl M. Bender
In this work we analyze PT-symmetric double-well potentials based on a two-mode picture. We reduce the problem into a PT-symmetric dimer and illustrate that the latter has effectively two fundamental bifurcations, a pitchfork (symmetry-breaking bifurcation) and a saddle-center one, which is the nonlinear analog of the PT-phase-transition. It is shown that the symmetry breaking leads to ghost states (amounting to growth or decay); although these states are not true solutions of the original continuum problem, the system’s dynamics closely follows them, at least in its metastable evolution. Past the second bifurcation, there are no longer states of the original continuum system. Nevertheless, the solutions can be analytically continued to yield a new pair of branches, which is also identified and dynamically examined. Our explicit analytical results for the dimer are directly compared to the full continuum problem, yielding a good agreement.
http://arxiv.org/abs/1207.1066
Pattern Formation and Solitons (nlin.PS); Quantum Gases (cond-mat.quant-gas); Mathematical Physics (math-ph)