In this talk I will discuss some recent progress made in the area of
non-linear dispersive PDEs, concerning the behavior of solitons and
multi-soliton solutions for non-integrable Korteweg-de Vries equations(KdV).
The main objective is to give a brief description of the
2-soliton collision for generalized KdV equations (Martel-Merle,
arXiv:0709.2672; M., arXiv:0903.1240).