Rogue Wave, Breathers and Bright-Dark-Rogue Solutions for the Coupled Schr(o)dinger Equations

摘要

We construct explicit rogue wave solutions,breather solitons,and rogue-bright-dark solutions for the coupled non-linear Schr(o)dinger equations by the Darboux transformation.The coupled non-linear Schr(o)dinger (CNLS/NLS)equations are a significant model in areas such as nonlinear optics,[1] bio-physics,[2] multi-component BoseEinstein condensates at zero temperature,[3] finance[4]and oceanics.[5] However,they become integrable for a special choice of the parameter (Manakov[6] model).On the other hand,the Manakov model has appeared in a Kerr-type approximation of photorefractive crystals.Therefore this equation can explicitly describe some physical phenomena.There is lots of the research about these kinds of system.[7-9]%We construct explicit rogue wave solutions, breather solitons, and rogue-bright-dark solutions for the coupled non-linear Schrodinger equations by the Darboux transformation.