  We study the global dynamics of the collision of two solitons having the same
mass for one-dimensional Nonlinear Schr\"odinger models with multi-power
nonlinearity. For any natural number k, it is verified that if the incoming
speed v between the two solitary waves is small enough, then, after the
collision, the two solitons will move away with an outcoming speed
v_{f}=v+O(v^{k}) and the remainder of the solution will also have energy and
weighted norms of order O(v^{k}). This is applied to the one-dimensional models
with polynomial odd nonlinearity having a stable soliton such as the cubic NLS
and the cubic-quintic NLS.
