Identifying coherent structures in nonlinear wave propagation.
Nonlinear wave phenomena are often characterized by the appearance of "solitary wave coherent structures" traveling at speeds determined by their amplitudes and morphologies. Assuming that time intervals exist in which these structures are essentially noninteracting, a method for identifying the number of independent features and their respective speeds is proposed and developed. The method is illustrated with a variety of increasingly realistic specific applications, beginning with a simple nonlinear but analytically tractable Gaussian model, continuing with (numerically generated) data describing multisoliton solutions to the Korteweg-de Vries equation, and concluding with (numerical) data from a realistic simulation of nonlinear wave interactions in plasma turbulence. These studies reveal both strengths and limitations of the method in its present incarnation and suggest topics for future investigations.