Discrete solitons in -symmetric lattices
1 Centro de Física Teórica e Computacional and Departamento de Física, Faculdade de Ciências, Universidade de Lisboa - Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal, EU
2 Department of Mathematics and Statistics, McMaster University - Hamilton, Ontario, L8S 4K1, Canada
Received: 28 September 2012
Accepted: 22 November 2012
We prove the existence of discrete solitons in infinite parity-time () symmetric lattices by means of analytical continuation from the anticontinuum limit. The energy balance between dissipation and gain implies that in the anticontinuum limit the solitons are constructed from elementary -symmetric blocks such as dimers, quadrimers, or more general oligomers. We consider in detail a chain of coupled dimers, analyze bifurcations of discrete solitons from the anticontinuum limit and show that the solitons are stable in a sufficiently large region of the lattice parameters. The generalization of the approach is illustrated on two examples of networks of quadrimers, for which stable discrete solitons are also found.
PACS: 63.20.Pw – Localized modes / 05.45.Yv – Solitons / 42.65.Wi – Nonlinear waveguides
© EPLA, 2012