Abstract
Via Darboux transformation method, breather and rogue wave solutions for the (2+1)-dimensional Hirota’s system will be derived. Meanwhile, the dynamic features of those solutions, as well as their various special superpositions creating different sequences of rogue wave due to the different simplest ratio of two frequencies, will be analytically and graphically analyzed. In addition, we will study the conversion mechanism, which can convert breathers and rogue waves into solitons and periodic waves. Through this conversion mechanism, we will obtain a range of stationary nonlinear waves such as M-shaped and W-shaped multi-peak solitons, (quasi) periodic waves and (quasi) anti-dark solitons that exhibit the stationary feature. By virtue of the second-order solutions, we will consider all possible semi-transformed waves, interactions between two non-parallel transformed waves and superpositions of two parallel transformed waves.
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