Ankiewicz, AdrianSoto-Crespo, Jose M.Chowdhury, M. AmdadulAkhmediev, Nail2014-11-052014-11-050740-3224http://hdl.handle.net/1885/12270Rogue waves in optical fibers can be mathematically described by the nonlinear Schrödinger equation and its extensions that take into account third-order dispersion, self-steepening, and self-frequency shift. These equations are integrable in special cases such as the Sasa–Satsuma or the Hirota equations. However, approximate polynomial solutions can also be obtained in cases beyond these integrable ones. We present these solutions and confirm their validity using numerical simulations.87-94© 2012 Optical Society of AmericaKeywords: Dinger equation; Hirota equation; Polynomial solution; Rogue waves; Self-frequency shift; Self-steepening; Third order dispersion; Electromagnetic dispersion; Frequency shift keying; Optical fibers; Polynomials; Nonlinear equations2013-0110.1364/JOSAB.30.0000872016-02-24