Helmholtz-Manakov solitons

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

Abstract

A novel spatial soliton-bearing wave equation is introduced, the Helmholtz-Manakov (H-M) equation, for describing the evolution of broad multi-component self-trapped beams in Kerr-type media. By omitting the slowly-varying envelope approximation, the H-M equation can describe accurately vector solitons propagating and interacting at arbitrarily large angles with respect to the reference direction. The H-M equation is solved using Hirota’s method, yielding four new classes of Helmholtz soliton that are vector generalizations of their scalar counterparts. General and particular forms of the three invariants of the H-M system are also reported.

Citation

Christian, J., McDonald, G., & Chamorro-Posada, P. (2006). Helmholtz-Manakov solitons. Physical Review E, 74(6), 066612. https://doi.org/10.1103/PhysRevE.74.066612

• Journal Article Type: Article
• Publication Date: Dec 28, 2006
• Deposit Date: Aug 22, 2007
• Publicly Available Date: Aug 22, 2007
• Journal: Physical Review E
• Print ISSN: 1539-3755
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 74
• Issue: 6
• Pages: 066612
• DOI: https://doi.org/10.1103/PhysRevE.74.066612
• Keywords: Optical solitons, optical Kerr effect
• Publisher URL: http://dx.doi.org/10.1103/PhysRevE.74.066612
• Related Public URLs: http://www.aps.org/; http://pre.aps.org/