Rogue waves in a resonant erbiumdoped fiber system with higherorder effects
Abstract
We mainly investigate a coupled system of the generalized nonlinear Schrödinger equation and the MaxwellBloch equations which describes the wave propagation in an erbiumdoped nonlinear fiber with higherorder effects including the forthorder dispersion and quintic nonKerr nonlinearity. We derive the onefold Darbox transformation of this system and construct the determinant representation of the $n$fold Darboux transformation. Then the determinant representation of the $n$th new solutions $(E^{[n]},\, p^{[n]},\, \eta^{[n]})$ which were generated from the known seed solutions $(E, \, p, \, \eta)$ is established through the $n$fold Darboux transformation. The solutions $(E^{[n]},\, p^{[n]},\, \eta^{[n]})$ provide the bright and dark breather solutions of this system. Furthermore, we construct the determinant representation of the $n$thorder 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2015
 DOI:
 10.48550/arXiv.1505.02237
 arXiv:
 arXiv:1505.02237
 Bibcode:
 2015arXiv150502237Z
 Keywords:

 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 Mathematical Physics;
 Physics  Optics
 EPrint:
 25 Pages Applied Mathematics and Computation 273(2016) 826841