  Three main topics were raised in this discussion session, which took place on
the 19th of June at the NumHyp-2015 meeting: nonlinear resonance for 1D systems
of balance laws, dispersive extensions of standard hyperbolic conservation
laws, and the validation of weakly dispersive shallow water wave models. An
introductory overview with many bibliographic references is provided for all
these topics. Based on kinetic formulation, a numerical strategy that can
overcome resonance issues is presented, and a well-balanced (WB) technique for
Vlasov-Fokker-Planck equations is outlined. This WB scheme relies on the
spectral representation of stationary solutions.
