The Whitham approach to dispersive shocks in systems with cubic–quintic nonlinearities

By employing a rigorous approach based on the Whitham modulation theory, we investigate dispersive shock waves arising in a high-order nonlinear Schr¨ odinger equation with competing cubic and quintic nonlinear responses. This model finds important applications in both nonlinear optics and Bose-Einstein condensates. Our theory predicts the formation of dispersive shocks with totally controllable properties, encompassing both steering and compression effects. Numerical simulations confirm these results perfectly. Quite remarkably, shock tuning can be achieved in the regime of a very small high order, i.e. quintic, nonlinearity.

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