Pure-Quartic Optical Shock Waves

Abstract

In this paper, we study the emergence and dynamics of pure-quartic optical dispersive shock waves governed by the nonlinear Schr\"odinger (NLS) equation with self-defocusing Kerr nonlinearity and fourth-order dispersion. The corresponding dispersionless hydrodynamic system reveals a distinct mechanism for wave breaking, driven by the nonlinear self-steepening of the hydrodynamic velocity. We illustrate this mechanism through optical dam-break configurations described by Riemann problems and show that, in contrast to the classical quadratic NLS equation, wave breaking occurs prior to wave splitting even in the small amplitude regime. Numerical simulations of the pure-quartic NLS (PQNLS) equation and its hydrodynamic approximation confirm these qualitatively distinct dynamical regimes.