Some singular limits for evolutionary Ginzburg–Landau equations

We give some partial results regarding to evolutionary dispersive Ginzburg–Landau equations associated to the static case considered in Béthuel, Brezis and Hélein [1]. We treat the partially dissipative case. Moreover we perform an exact “semi-classical” limit. We obtain alternatively the Laplace, heat and wave equations as limit equation, depending on the scaling that we consider.