Phase Diffusion and Weak Turbulence
University of Arizona
In this expository talk, I will first review the different kinds of phase instabilities (Eckhaus, zig-zag, Benjamin-Feir) observed in generic envelope equations. I will then discuss how the dynamics of a complex order-parameter can be reduced to that of a phase equation and introduce the concept of phase turbulence. The last part of the talk will be devoted to weak turbulence in the one- and two-dimensional complex Ginzburg-Landau equation, and to its link to the Benjamin-Feir instability.