As it is well known, there is a huge number of partial differential equations with a recognized physical relevance used to describe the nonlinear wave evolution (equations like the KdV, the Schrödinger, the Benjamin-Ono, the Benjamin-Bona-Mahony, the KP, some Boussinesq systems, the Benney-Luke models, among). Many of these models have a Hamiltonian structure and also are derived via an asymptotic analysis by imposing in models with a major complexity some restriction on the amplitude parameter or in the wave length parameter, for example.

The aim of this mini-symposium is to present for these models results of existence of travelling wave solutions (periodic or solitary waves), existence and uniqueness for the Cauchy Problem, unique continuation, stability of travelling waves, inverse scattering, among others.