Abstract
The nonlinear Schrodinger equation (NLSE) is one of the key equations in physics. It describes the evolution in time and space of wave packets and it applies to several nonlinear dispersive media, such as Bose-Einstein condensates, plasma, optics and hydrodynamics. An important feature of the NLSE is its integrability. Exact solutions and their experimental observations, ranging from solitons to breathers in various physical media, confirmed the validity of the NLSE in accurately describing the wave motion. The accuracy is surprisingly high even for the cases of severe wave focusing in a wide range of nonlinear dispersive media. In this Chapter, we will briefly discuss the physical relevance of exact NLSE solutions as well as review past and recent progress of experimental studies of dark and bright NLSE solutions in hydrodynamics. Validity and limitations of such weakly nonlinear models will be discussed in detail. Related promising engineering applications will be also emphasized.
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