N-order bright and dark rogue waves in a Resonant erbium-doped Fibre system
The rogue waves in a resonant erbium-doped fibre system governed by a coupled system of the nonlinear Schr\"odinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the breather solutions of the normalized slowly varying amplitud...
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| description | The rogue waves in a resonant erbium-doped fibre system governed by a coupled system of the nonlinear Schr\"odinger equation and the Maxwell-Bloch equation (NLS-MB equations) are given explicitly by a Taylor series expansion about the breather solutions of the normalized slowly varying amplitude of the complex field envelope \(E\), polarization \(p\) and population inversion \(\eta\). The n-order breather solutions of the three fields are constructed using Darboux transformation (DT) by assuming periodic seed solutions. What is more, the n-order rogue waves are given by determinant forms with \(n+3\) free parameters. Furthermore, the possible connection between our rouge waves and the generation of supercontinuum generation is discussed. |
| doi_str_mv | 10.48550/arxiv.1210.2522 |
| format | Article |
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The n-order breather solutions of the three fields are constructed using Darboux transformation (DT) by assuming periodic seed solutions. What is more, the n-order rogue waves are given by determinant forms with \(n+3\) free parameters. Furthermore, the possible connection between our rouge waves and the generation of supercontinuum generation is discussed.</description><identifier>EISSN: 2331-8422</identifier><identifier>DOI: 10.48550/arxiv.1210.2522</identifier><language>eng</language><publisher>Ithaca: Cornell University Library, arXiv.org</publisher><subject>Doped fibers ; Erbium ; Mathematics - Mathematical Physics ; Physics - Exactly Solvable and Integrable Systems ; Physics - Mathematical Physics ; Population inversion ; Series expansion ; Taylor series</subject><ispartof>arXiv.org, 2012-12</ispartof><rights>2012. This work is published under http://creativecommons.org/licenses/by-nc-sa/3.0/ (the “License”). 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| subjects | Doped fibers Erbium Mathematics - Mathematical Physics Physics - Exactly Solvable and Integrable Systems Physics - Mathematical Physics Population inversion Series expansion Taylor series |
| title | N-order bright and dark rogue waves in a Resonant erbium-doped Fibre system |
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