I will present two cases of strong interactions between solitary waves for the nonlinear Schrödinger equations (NLS). In the mass sub- and super-critical cases, a work by Tien Vinh Nguyen proves the existence of multi-solitary waves with logarithmic distance in time, extending a classical result of the integrable case (1D cubic NLS equation). In the mass-critical case, a work by Yvan Martel and Pierre Raphaël gives a new class of blow up multi-solitary waves blowing up in infinite time with logarithmic rate.
These special behaviours are due to strong interactions between the waves, in contrast with most previous works on multi-solitary waves of (NLS) where interactions do not affect the general behaviour of each solitary wave.[-]

It is possible to model dissipation effects subjected by a particle by interactions between the particle and its environment. This seminal idea dates back to Caldeira-Leggett in the '80ies. The specific case of a particle interacting with vibrational degrees of freedom has been thoroughsly investigated by S. De Bièvre and his collaborators. We will go back to these issues in the framework of kinetic equations, and also consider quantum versions of the problem based on couplings with the Schrödinger equation. We are particularly interested in stability issues. We will describe ; through rigorous statements and numerical experiments, analogies and differences with the case of a single classical particle and with the standard coupling with the Poisson equation.[-]