The Choi–Williams Analysis of the Non-Linear Wave Processes

Abstract

The nonlinear wave process has been analysed with the Choi–Williams transform which belongs to the Cohen transforms class. The models of shock waves, classical soliton, soliton of envelope, solution of Burgers–Kortewegde Vries equation, i.e. the centaur solution, and models of cnoidal and saw-tooth waves are studied. The results of Choi–Williams-, Wignerand Fourier-analysis are compared. The aforesaid transforms are shown to well supplement each other and when used together allow to acquire more information about the investigated signals or processes.