Soliton Molecules and Some Hybrid Solutions for the Nonlinear Schr?dinger Equation

Based on velocity resonance and Darboux transformation, soliton molecules and hybrid solutions consisting of soliton molecules and smooth positons are derived. Two new interesting results are obtained: the first is that the relationship between soliton molecules and smooth positons is clearly pointed out, and the second is that we find two different interactions between smooth positons called strong interaction and weak interaction, respectively. The strong interaction will only disappear when t \to \infty. This strong interaction can also excite some periodic phenomena.