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In this paper, the extended nonlinear Schrödinger equation with higher-order operators, which can be diffusely used to describe the pulses propagating along an optical fibre, is under investigation. By means of the generalized Darboux transformation, we present the interactional solutions composed of the breather and rogue wave. Furthermore, regulating the coefficients of higher-order operators results in miscellaneous patterns of the interactions between the breather and rogue wave. Especially, the solutions in the extended nonlinear Schrödinger equation are more abundant than ones in the classical nonlinear Schrödinger equation. The kinetics of interactional solutions are elucidated graphically. The method provided in this paper can also be adopted to construct interactional solutions of other higher-order nonlinear integrable equations.

Interactional solutions of the extended nonlinear Schrödinger equation with higher-order operators