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

## Abstract

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.

- Authors:

- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515 (United States)
- Department of Physics, University of Athens, Panepistimiopolis, Zografos, Athens 15784 (Greece)
- Department of Interdisciplinary Studies, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978 (Israel)

- Publication Date:

- OSTI Identifier:
- 21072284

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 1; Other Information: DOI: 10.1103/PhysRevE.75.016607; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOSE-EINSTEIN CONDENSATION; CRYSTAL LATTICES; CRYSTALS; NONLINEAR PROBLEMS; PHOTONS; SOLITONS; STABILITY; THREE-DIMENSIONAL CALCULATIONS; TRAPPING; TWO-DIMENSIONAL CALCULATIONS; WAVE FORMS

### Citation Formats

```
Kevrekidis, P. G., Gagnon, J., Frantzeskakis, D. J., and Malomed, B. A.
```*X, Y, and Z waves: Extended structures in nonlinear lattices*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.016607.

```
Kevrekidis, P. G., Gagnon, J., Frantzeskakis, D. J., & Malomed, B. A.
```*X, Y, and Z waves: Extended structures in nonlinear lattices*. United States. doi:10.1103/PHYSREVE.75.016607.

```
Kevrekidis, P. G., Gagnon, J., Frantzeskakis, D. J., and Malomed, B. A. Mon .
"X, Y, and Z waves: Extended structures in nonlinear lattices". United States.
doi:10.1103/PHYSREVE.75.016607.
```

```
@article{osti_21072284,
```

title = {X, Y, and Z waves: Extended structures in nonlinear lattices},

author = {Kevrekidis, P. G. and Gagnon, J. and Frantzeskakis, D. J. and Malomed, B. A.},

abstractNote = {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.},

doi = {10.1103/PHYSREVE.75.016607},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 1,

volume = 75,

place = {United States},

year = {Mon Jan 15 00:00:00 EST 2007},

month = {Mon Jan 15 00:00:00 EST 2007}

}

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