Abstract
In this paper, we will investigate nonlinear waves, such as solitons, breathers and rogue waves, that coexist and interact with each other under different backgrounds for a higher-order coupled nonlinear Schrödinger (HNLS) system. Under the unequal or equal phase position, we can observe rogue waves which coexist with solitons or breathers. Moreover, under the equal phase position, we can get higher-order nonlinear waves. At the same time, we will observe different transformations that occur between those localized waves with the parameters changing. For instance, when the amplitude of one of the seed solutions tends to zero, the breathers part will transform into solitons and the peak of one of the rogue waves will become ultra-small. Under the periodic background, we will also investigate the interactions between distinct types of localized wave solutions.
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