Extreme wave solutions: Parametric studies and wavelet analysis

Abstract Wave fields for near homoclinic, single mode rogue-wave solutions of the periodic nonlinear Schrodinger equation are presented. Parameters of candidate solutions are estimated and refined through an eigenvalue solution procedure. An overview of the estimation and refining procedure used by the authors is provided. Solutions are scaled to facilitate experimental implementation. The continuous wavelet transform is used to carry out time–frequency analyses and the results obtained are demonstrative of the dispersion relation as well as the time varying side band energy transfer associated with the Benjamin–Feir instability. The analysis framework and approach used are validated with the Peregrine solution. Other extreme wave solutions are analyzed as well. The framework presented here could serve as a basis for experimental investigations into single mode rogue waves as well as other localizations in wave fields.