Destabilization and localization of traveling waves by an advected field (Q5947018)

The authors consider traveling waves arising in a supercritical Hopf bifurcation coupled to a real, slowly varying field. The field is advected by the waves and, in turn, can affect the dynamics of the waves through coupling to their growth rate. Moreover, they also deal with characterizing the linear and nonlinear behaviours of the phase and amplitude instabilities, respectively. In both cases they derive an envelope equation for the instability near its threshold and compare the results to full numerical simulations of the original equations.