Akhmediev breathers, Ma solitons, and general breathers from rogue waves: A case study in the Manakov system

摘要

We present explicit forms of general breather (GB), Akhmediev breather (AB), Ma soliton (MS), and roguenwave (RW) solutions of the two-component nonlinear Schr¨odinger (NLS) equation, namely Manakov equation.nWe derive these solutions through two different routes. In the forward route, we first construct a suitable periodicnenvelope soliton solution to this model from which we derive GB, AB, MS, and RWsolutions.We then considernthe RW solution as the starting point and derive AB, MS, and GB in the reverse direction. The second approachnhas not been illustrated so far for the two component NLS equation. Our results show that the above rationalnsolutions of the Manakov system can be derived from the standard scalar nonlinear Schr¨odinger equation with anmodified nonlinearity parameter. Through this two-way approach we establish a broader understanding of thesenrational solutions, which will be of interest in a variety of situations.