Staggered -symmetric ladders with cubic nonlinearity
arXiv:1409.7413 · doi:10.1103/PhysRevE.91.033207
Abstract
We introduce a ladder-shaped chain with each rung carrying a -symmetric gain-loss dipole. The polarity of the dipoles is staggered along the chain, meaning that a rung bearing gain-loss is followed by one bearing loss-gain. This renders the system -symmetric in both horizontal and vertical directions. The system is governed by a pair of linearly coupled discrete nonlinear Schrödinger (DNLS) equations with self-focusing or defocusing cubic onsite nonlinearity. Starting from the analytically tractable anti-continuum limit of uncoupled rungs and using the Newton's method for identifying solutions and parametric continuation in the inter-rung coupling for following the associated branches, we construct families of -symmetric discrete solitons and identify their stability regions. Waveforms stemming from a single excited rung, as well as ones from multiple rungs are identified. Dynamics of unstable solitons is presented too.
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