Binary Darboux transformation, solitons and breathers for a second-order three-wave resonant interaction system

In this paper, a second-order three-wave interaction system, which belongs to a three-wave resonant interaction hierarchy, is investigated. Based on a known Lax pair, we firstly derive a binary Darboux transformation and the Nth-order analytic solutions with symbolic computation, where N is a positive integer. Behaviors of the one soliton are studied, and then, multi solitons and bound-state solitons on the zero background are investigated. When we select two of the three seed solutions as 0, the Nth-order analytic solutions describe the interactions among the breathers and three kinds of the dark-bright solitons. Moreover, we explore the influence of certain parameters on the interactions among the breathers and three kinds of the dark-bright solitons. With less than two of the three seed solutions selected as 0, the breathers and bound-state breathers are derived via the Nth-order analytic solutions.