Helmholtz algebraic solitons

Christian, JM; McDonald, GS; Chamorro-Posada, P

Abstract

We report, to the best of our knowledge, the first exact analytical algebraic solitons of a generalized cubic-quintic Helmholtz equation. This class of governing equation plays a key role in photonics modelling, allowing a full description of the propagation and interaction of broad scalar beams. New conservation laws are presented, and the recovery of paraxial results is discussed in detail. The stability properties of the new solitons are investigated by combining semi-analytical methods and computer simulations. In particular, new general stability regimes are reported for algebraic bright solitons.

Citation

Christian, J., McDonald, G., & Chamorro-Posada, P. (2010). Helmholtz algebraic solitons. Journal of Physics A: Mathematical and Theoretical, 43(8), https://doi.org/10.1088/1751-8113/43/8/085212

• Journal Article Type: Article
• Publication Date: Jan 1, 2010
• Deposit Date: Feb 8, 2010
• Publicly Available Date: Apr 5, 2016
• Journal: Journal of Physics A: Mathematical and Theoretical
• Print ISSN: 1751-8113
• Publisher: IOP Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 43
• Issue: 8
• DOI: https://doi.org/10.1088/1751-8113/43/8/085212
• Publisher URL: http://dx.doi.org/ 10.1088/1751-8113/43/8/085212
• Related Public URLs: http://www.iop.org/EJ/JPhysA