Breathers and solitons of generalized nonlinear Schr\"odinger equations as degenerations of algebro-geometric solutions

We present new solutions in terms of elementary functions of the multi-component nonlinear Schr\"odinger equations and known solutions of the Davey-Stewartson equations such as multi-soliton, breather, dromion and lump solutions. These solutions are given in a simple determinantal form and are obtained as limiting cases in suitable degenerations of previously derived algebro-geometric solutions. In particular we present for the first time breather and rational breather solutions of the multi-component nonlinear Schr\"odinger equations.