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

摘要

We present explicit forms of general breather (GB), Akhmediev breather (AB),Ma soliton (MS) and rogue wave (RW) solutions of the two component nonlinearSchr\"{o}dinger (NLS) equation, namely Manakov equation. We derive thesesolutions through two different routes. In the forward route we first constructa suitable periodic envelope soliton solution to this model from which wederive GB, AB, MS and RW solutions. We then consider the RW solution as thestarting point and derive AB, MS and GB in the reverse direction. The secondapproach has not been illustrated so far for the two component NLS equation.Our results show that the above rational solutions of the Manakov system can bederived from the standard scalar nonlinear Schr\"{o}dinger equation with amodified nonlinearity parameter. Through this two way approach we establish abroader understanding of these rational solutions which will be of interest ina variety of situations.