Statistics and Characteristics of Spatiotemporally Rare Intense Events in Complex Ginzburg-Landau Models

Phys. Rev. E 67, 026203 (2003)https://ireap.umd.edu/10.1103/PhysRevE.67.0262032003Journal ArticleComplex and Emergent Systems

We study the statistics and characteristics of rare intense events in two types of two-dimensional complex Ginzburg-Landau (CGL) equation based models. Our numerical simulations show finite amplitude collapselike solutions which approach the infinite amplitude solutions of the nonlinear Schrödinger equation in an appropriate parameter regime. We also determine the probability distribution function of the amplitude of the CGL solutions, which is found to have enhanced (as compared to Gaussian) probability for the amplitude to be large. Our results suggest a general picture in which an incoherent background of weakly interacting waves, occasionally, “by chance,” initiates intense, coherent, self-reinforcing, highly nonlinear events.