Formation of dispersive shock waves in a saturable nonlinear medium

TL;DR

This paper investigates the formation of dispersive shock waves in a saturable nonlinear medium using the Whitham averaging method, extending previous models to more realistic initial conditions and deriving measurable shock characteristics.

Contribution

It generalizes the analysis of dispersive shock waves to saturable media with realistic initial pulses, providing a way to predict observable shock features.

Findings

Derived shock edge positions and intensities for realistic initial conditions

Determined wave-breaking time in saturable nonlinear media

Extended previous models to more practical experimental setups

Abstract

We use the Gurevich-Pitaevskii approach based on the Whitham averaging method for studying the formation of dispersive shock waves in an intense light pulse propagating through a saturable nonlinear medium. Although the Whitham modulation equations cannot be diagonalized in this case, the main characteristics of the dispersive shock can be derived by means of an analysis of the properties of these equations at the boundaries of the shock. Our approach generalizes a previous analysis of step-like initial intensity distributions to a more realistic type of initial light pulse and makes it possible to determine, in a setting of experimental interest, the value of measurable quantities such as the wave-breaking time or the position and light intensity of the shock edges.