 Rogue waves in a resonant erbium-doped fiber system with higher-order effectsYu Zhang, Chuanzhong Li and Jingsong He Applied Mathematics and Computation, 2016, vol. 273, issue C, 826-841 Abstract: We mainly investigate a coupled system of the generalized nonlinear Schrödinger equation and the Maxwell–Bloch equations which describes the wave propagation in an erbium-doped nonlinear fiber with higher-order effects including the forth-order dispersion and quintic non-Kerr nonlinearity. We derive the one-fold Darboux transformation of this system and construct the determinant representation of the n-fold Darboux transformation. Then the determinant representation of the nth new solutions (E[n], p[n], η[n]) which were generated from the known seed solutions (E, p, η) is established through the n-fold Darboux transformation. The solutions (E[n], p[n], η[n]) provide the bright and dark breather solutions of this system. Furthermore, we construct the determinant representation of the nth-order bright and dark rogue waves by Taylor expansions and also discuss the hybrid solutions which are the nonlinear superposition of the rogue wave and breather solutions. Keywords: Generalized nonlinear Schrödinger and Maxwell–Bloch system; Darboux transformation; Breathers; Rogue waves; Hybrid solutions (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:273:y:2016:i:c:p:826-841 DOI: 10.1016/j.amc.2015.10.015 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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