Nonlinear wave solutions for an integrable sixth-order nonlinear Schrödinger equation in an optical fiber

Under investigation in this paper is an integrable sixth-order nonlinear Schrödinger equation. Multi-soliton and higher-order breather solutions are obtained via the Darboux transformation. The higher-order rogue-wave solutions are derived via the generalized Darboux transformation. Effects of the higher-order terms on the interaction and propagation of the solitons, breathers and rogue waves are discussed graphically. Interactions between/among the solitons are elastic because the soliton amplitudes keep unchanged except for some phase shifts. In addition, the higher-order terms could enhance the steepness of the solitons. Periods of the Kuznetsov-Ma breathers are only related to the spectral parameter. Periods of the Akhmediev breathers are not only related to the spectral parameter, but also related to the coefficients of the higher-order terms. Akhmediev breathers have the phase shifts after the interaction, while Kuznetsov-Ma breathers have no phase shifts. The higher-order terms could enhance the steepness and symmetry of the rogue waves.