X,Y,Z-Waves: Extended Structures in Nonlinear Lattices

TL;DR

This paper introduces multi-legged extended nonlinear structures in 2D and 3D lattices, analyzing their stability and potential physical applications in systems like Bose-Einstein condensates and photorefractive crystals.

Contribution

It proposes a new class of extended waveforms in nonlinear lattices, combining analytical stability analysis with numerical construction of these structures.

Findings

Analytical stability of the structures established.

Numerical models of the extended structures developed.

Potential relevance to various physical systems identified.

Abstract

Motivated by recent experimental and theoretical results on optical X-waves, we propose a new type of waveforms in 2D and 3D discrete media -- multi-legged extended nonlinear structures (ENS), built as arrays of lattice solitons (tiles or stones, in the 2D and 3D cases, respectively). First, 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. The predicted patterns are relevant to a variety of physical settings, such as Bose-Einstein condensates in deep optical lattices, lattices built of microresonators, photorefractive crystals with optically induced lattices (in the 2D case) and others.