I. V. Barashenkov, Sergey V. Suchkov, Andrey A. Sukhorukov, Sergey V. Dmitriev, Yuri S. Kivshar
We show that the parity-time (PT) symmetric coupled optical waveguides with gain and loss support localised oscillatory structures similar to the breathers of the classical \(\phi^4\) model. The power carried by the PT-breather oscillates periodically, switching back and forth between the waveguides, so that the gain and loss are compensated on the average. The breathers are found to coexist with solitons and be prevalent in the products of the soliton collisions. We demonstrate that the evolution of the small-amplitude breather’s envelope is governed by a system of two coupled nonlinear Schrodinger equations, and employ this Hamiltonian system to show that the small-amplitude PT-breathers are stable.
http://arxiv.org/abs/1211.1835
Pattern Formation and Solitons (nlin.PS); Optics (physics.optics)
Sergey V. Suchkov, Boris A. Malomed, Sergey V. Dmitriev, Yuri S. Kivshar
Dynamics of a chain of interacting parity-time invariant nonlinear dimers is investigated. A dimer is built as a pair of coupled elements with equal gain and loss. A relation between stationary soliton solutions of the model and solitons of the discrete nonlinear Schrodinger (DNLS) equation is demonstrated. Approximate solutions for solitons whose width is large in comparison to the lattice spacing are derived, using a continuum counterpart of the discrete equations. These solitons are mobile, featuring nearly elastic collisions. Stationary solutions for narrow solitons, which are immobile due to the pinning by the effective Peierls-Nabarro potential, are constructed numerically, starting from the anti-continuum limit. The solitons with the amplitude exceeding a certain critical value suffer an instability leading to blowup, which is a specific feature of the nonlinear PT-symmetric chain, making it dynamically different from DNLS lattices. A qualitative explanation of this feature is proposed. The instability threshold drops with the increase of the gain-loss coefficient, but it does not depend on the lattice coupling constant, nor on the soliton’s velocity.
http://arxiv.org/abs/1110.1501
Optics (physics.optics)