Chess-Board-Like Spatio-Temporal Interference Patterns and Their Excitation

TL;DR

This paper uncovers new chess-board-like interference patterns in the nonlinear Schrödinger equation, arising from breather collisions and initial conditions, with implications across optics, hydrodynamics, and quantum fluids.

Contribution

It introduces a novel class of spatio-temporal interference patterns in the NLSE, linking them to continuous spectrum bands and complex initial conditions.

Findings

Chess-board-like patterns occur at special conditions in NLSE.

Patterns result from breather collisions and initial conditions.

Patterns are observable in various physical systems.

Abstract

We discover new type of interference patterns generated in the focusing nonlinear Schr\"odinger equation (NLSE) with localised periodic initial conditions. At special conditions, found in the present work, these patterns exhibit novel chess-board-like spatio-temporal structures which can be observed as the outcome of collision of two breathers. The infinitely extended chess-board-like patterns correspond to the continuous spectrum bands of the NLSE theory. More complicated patterns can be observed when the initial condition contains several localised periodic swells. These patterns can be observed in a variety of physical situations ranging from optics and hydrodynamics to Bose-Einstein condensates and plasma.