X, Y, and Z waves: Extended structures in nonlinear lattices

P. G. Kevrekidis*, J. Gagnon, D. J. Frantzeskakis, B. A. Malomed

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


We propose a new type of waveforms in two-dimensional (2D) and three-dimensional (3D) discrete media-multilegged extended nonlinear structures (ENSs), built as arrays of lattice solitons (tiles and stones, in the 2D and 3D cases, respectively). We study the stability of the tiles and stones analytically, and then extend them numerically to complete ENS forms for both 2D and 3D lattices, aiming to single out stable ENSs. The predicted patterns can be realized in Bose-Einstein condensates trapped in deep optical lattices, crystals built of microresonators, and 2D photonic crystals. In the latter case, the patterns provide for a technique for writing reconfigurable virtual partitions in multipurpose photonic devices.

Original languageEnglish
Article number016607
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
StatePublished - 2007


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