Staggered dispersions: Part I. Shocliton, quantum revival and fractalization

TL;DR

This paper introduces the concept of staggered dispersions in nonlinear wave equations, revealing their role in supporting bi-directional waves, fractalization, and quantum revival phenomena, thus offering new insights into wave dynamics.

Contribution

It presents a novel approach of alternating frequency signs in nonlinear wave equations to control dispersive shock behavior and induce fractal and quantum revival effects.

Findings

Staggered dispersions support bi-directional wave propagation.

They can induce fractalization in wave patterns.

They facilitate quantum revival phenomena like the Talbot effect.

Abstract

Alternating the signs of the frequencies for Fourier components with even and odd (normalized) wavenumbers in the nonlinear-wave, such as the Korteweg-de Vries, equations maintains a constantly drifting dispersive shock with similar solitonic oscillations on both sides, like some plasma and quantum shocks. Such \textit{staggered dispersions} support bi-directional waves and can symmetrize and deregularize (to some degree) the nonlinear dynamics, with physical consequences that can also be reflected in the fractalization and quantum revival (Talbot effect).