Various rational solutions generated from the higher order Kaup–Newell type equation

Abstract

The types of soliton interactions, such as weak interactions, strong interactions, stable new local waves and rogue waves, are very rich. Considering the extremely rich soliton type solutions, for example, bright or dark solitons, phase solutions and breather solutions, in the higher order Kaup–Newell type equation which can describe the waves propagation in optical and plasma system, the analysis of the interactions between various solutions is helpful for constructing new solutions and explaining new phenomena. Compared with the previous research results, we mainly focus on the following two aspects: (i) The higher order term plays a unique role in the formation of rational solutions; (ii) The various rational solutions are generated from the synchronized and resonant interactions of multiple solitons. These studies mainly elaborate on the formation of large amplitude waves, such as rogue waves, rational W-shape solitons, and rational dark or bright solitons, in terms of boundary conditions, the number of soliton interactions, spectral parameters and the higher order terms in this equation.