Dispersive Lamb Systems

Under periodic boundary conditions, a one-dimensional dispersive medium driven by a Lamb oscillator exhibits a smooth response when the dispersion relation is asymptotically linear or superlinear at large wave numbers, but unusual fractal solution profile emerge when the dispersion relation is asymptotically sublinear. Strikingly, this is precisely the opposite to the superlinear asymptotic regime required for fractalization and dispersive quantization, also known as the Talbot effect, of the unforced medium produced by discontinuous initial conditions.