Higher-order breathers and breather interactions for the AB system in fluids

In this paper, we perform a systematical study on the breathers of the AB system in fluids. The expressions of the first- to third-order breather solutions are explicitly computed through applying the Darboux transformation method to the system. Some new and interesting features for the breathers are found out as follows. Firstly, in addition to the general breathers, Ak-breathers and Ma-breathers are observed. Further, the corresponding spectrum parameter constrains to form the three breathers are given. Secondly, the dependent variables A and B in the system possess a few of novel spatio-temporal patterns for the periodical wave packets which form the breathers: two-petals, three-petals and four-petals. Thirdly, the interactions between two- or multiple-breathers are elastic. Lastly, there are rich interaction patterns, such as, Ak-breathers and Ma-breather cross vertically, breathers parallel with the same speed.