Pair-Tunneling Induced Localized Waves in a Vector Nonlinear Schr\"{o}dinger Equation

We investigate the localized waves of the coupled two-mode nonlinear Schr\"{o}dinger equations with a pair-tunneling term representing strongly interacting particles can tunnel between the modes as a fragmented pair. Facilitated by Darboux transformation, we have derived exact solution of nonlinear vector waves such as bright solitons, Kuznetsov-Ma soliton, Akhmediev breathers and rogue waves and demonstrated their interesting temporal-spatial structures. The phase diagram that demarcates the parameter ranges of the nonlinear waves is obtained. Our results have implications in such diverse fields as Bose-Einstein condensate, nonlinear fibers and super fluids.