Obtaining real long-lived Bragg solitons via wave-packet reflection from smoothly increasing periodic barriers

Establish whether real long-lived Bragg solitons can be obtained by exciting a quasi-monochromatic long surface gravity wave packet that interacts with and reflects from a region of smoothly increasing height of a periodic array of bottom barriers, within the fully nonlinear exact free-surface equations in conformal variables.

Background

The authors numerically model fully nonlinear potential flows in conformal variables over strongly inhomogeneous periodic bottoms and observe strong nonlinear compression of an incoming wave packet near the upper edge of the bandgap, forming a short and high packet of nearly standing waves with sharp crests that subsequently transforms into a backward-propagating wave.

Despite these findings, they explicitly state that they were unable to obtain genuine long-lived Bragg solitons by this method, as the high wave group reflects instead of penetrating further into the barrier region, and they call for continued investigation of this problem.