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Bistable dark solitons of a cubic-quintic Helmholtz equation

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

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P Chamorro-Posada


We report, to the best of our knowledge, the first exact analytical bistable dark spatial solitons of a nonlinear Helmholtz equation with a cubic-quintic refractive-index model. Our analysis begins with an investigation of the modulational instability characteristics of Helmholtz plane waves. We then derive a dark soliton by mapping the desired asymptotic form onto a uniform background field, and obtain a more general solution by deploying rotational invariance laws in the laboratory frame. The geometry of the new soliton is explored in detail, and a range of new physical predictions is uncovered. Particular attention is paid to the unified phenomena of arbitrary-angle off-axis propagation and non-degenerate bistability. Crucially, the corresponding solution of paraxial theory emerges in a simultaneous multiple limit. We conclude with a set of computer simulations that examine the role of Helmholtz dark solitons as robust attractors.


Christian, J., McDonald, G., & Chamorro-Posada, P. (2010). Bistable dark solitons of a cubic-quintic Helmholtz equation. Physical Review A, 81(5),

Journal Article Type Article
Publication Date May 1, 2010
Deposit Date Apr 15, 2010
Publicly Available Date Apr 5, 2016
Journal Physical Review A (PRA)
Print ISSN 1050-2947
Publisher American Physical Society
Peer Reviewed Peer Reviewed
Volume 81
Issue 5
Publisher URL 10.1103/PhysRevA.81.053831


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