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

Abstract

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.