# 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.

## Key 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).

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Source: https://tomesphere.com/paper/2302.12025