KAUST University , Saudi Arabia

Dispersive shock waves are ubiquitous phenomena originated by the regularization of wave breaking of nonlinear waves. Wave breaking, in turn, is characterized by the formation of singular and multivalued regions that, in dispersive media, act as precursors for the generation of periodic nonlinear wavetrains (i.e., cnoidal waves), whose dynamics defines the dispersive shock. In this talk I will review my activity in the field, discussing various theoretical approaches to the problem, including the Whitham theory of modulation and new statistical mechanics frameworks based on the thermodynamics of chaos. I will also discuss the implications of shock waves on the complexity of Soliton waves.