Shock Waves

We discuss the physics of shock waves with special emphasis on the phenomena related to the field of nonlinear fiber optics. We first introduce the general mechanism commonly known as gradient catastrophe and the related concept of classical shock waves. Then we proceed to discuss the possible regularizationmechanisms of the shock, and in particular the dispersive regularization, which is behind the formation of dispersive shock waves in fibers. We then discuss different possible scenarios that lead to observe the formation of dispersive shock waves in fibers, such as pulse propagation, four-wave mixing, and passive resonators, also showing that fibers allow for investigating the dispersive regime of classical problems related to the physics of shock such as the dam break problem and the propagation of Riemann waves.We also discuss the phase-matchingmechanism that induces the shock to efficiently radiate resonant radiation in the normal dispersion regime. Throughout the text we refer to the mathematical models and the approaches that are employed to describe such phenomenona.