Hydrodynamics of Exact Nonlinear Schrodinger Equation Solutions - Theory and Experiments
The dynamics of water waves in finite as well as in infinite water depth conditions can be approximated by the nonlinear Schrodinger equation (NLSE). The particularity of the NLSE is it integrability. In fact, it admits a family of stationary and pulsating solutions, the latter are also referred to as breathers solutions. Breathers describe different stages of the modulation instability process, therefore, the dynamics of extreme waves. The observation of breather solutions in different nonlinear dispersive media attracted the scientic interest recently. Here, novel laboratory experiments, conducted in several wave facilities, on stationary and pulsating NLSE solutions, including multidirectionality are presented. Observed characteristic properties, related to NLSE localizations are highlighted. Furthermore, a range of applications as well as model limitations are emphasized and discussed in detail.