Kinetic Theory of Solitons and Quasi-Particles

We compare two different approaches to turbulence: the kinetic theory of solitons and the kinetic theory of quasi-particles. Using the same model equation as the starting point of both descriptions, we compare their properties, advantages, and limitations. We also address the question of whether a gas of solitons be seen as a particular case of a gas of quasi-particles and propose possible strategies leading to a more general theoretical model of wave turbulence.