Helmholtz bright and boundary solitons

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

Abstract

We report, for the first time, exact analytical boundary solitons of a generalized cubic-quintic Non-Linear Helmholtz (NLH) equation. These solutions have a linked-plateau topology that is distinct from conventional dark soliton solutions; their amplitude and intensity distributions are spatially delocalized and connect regions of finite and zero wave-field disturbances (suggesting also the classification as 'edge solitons'). Extensive numerical simulations compare the stability properties of recently-reported Helmholtz bright solitons, for this type of polynomial non-linearity, to those of the new boundary solitons. The latter are found to possess a remarkable stability characteristic, exhibiting robustness against perturbations that would otherwise lead to the destabilizing of their bright-soliton counterparts

Citation

Christian, J., McDonald, G., & Chamorro-Posada, P. (2007). Helmholtz bright and boundary solitons. Journal of Physics A: Mathematical and Theoretical, 40(7), 1545-1560. https://doi.org/10.1088/1751-8113/40/7/008

• Journal Article Type: Article
• Publication Date: Jan 30, 2007
• Deposit Date: Oct 14, 2011
• 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: 40
• Issue: 7
• Pages: 1545-1560
• DOI: https://doi.org/10.1088/1751-8113/40/7/008
• Publisher URL: http://dx.doi.org/ 10.1088/1751-8113/40/7/008
• Related Public URLs: http://www.cse.salford.ac.uk/profiles/gsmcdonald/36_J_Phys_A_Math_Theor_40_1545_2007.pdf