Shock generation is a leading topic in nonlinear physics and optics. Shock waves occur whenever one enters highly nonlinear regimes either in time or in space. The origin of the undular bores is among the mysterious dynamics of shock wave generation. The undular bores are the fast oscillations that regularize the wave-breaking after the shock; their features are very difficult to understand theoretically.
A typical phenomenon is the appearance of the Batman ears in the optical intensity when the shock occurs; these “ears” are very pronounced peaks limiting the region of the shock and including undulars bores. Figures above show the Batman ears in the far field of a shock wave genereated in the spatial nonlinear optical propagation. Beyond numerical simulations, we do not have a complete theoretical description of this effect.
In a paper published in Optics Express (arXiv:1601.05796)Maria Chiara Braidotti, Silvia Gentilini, and Claudio Conti show that Gamow vectors of the reversed harmonic oscillator provide a new theoretical tool for the quantitative description of spatial shock waves in nonlocal media. The analytical calculations perfectly reproduce our experiments. This opens a number of possibilities for describing and controlling the shock waves in highly nonlocal and non-instantaneous media. The results also show the validity of the novel theoretical methods inherited by the so-called “time-asymmetric quantum-mechanics.”
The picture above shows the comparison between experiments and the analytically calculated Gamow vectors.