# Formation of nonlinear X-waves in condensed matter systems

## TL;DR

This paper investigates the formation of nonlinear X-waves in condensed matter systems, demonstrating their origin from wave packet interference in systems with hyperbolic dispersion and nonlinear interactions, with potential observations in spin-orbit coupled BECs.

## Contribution

It reveals the mechanism behind polariton X-wave formation and predicts similar structures in spin-orbit coupled Bose-Einstein condensates.

## Key findings

- X-waves result from interference of wave packets in hyperbolic dispersion systems
- Nonlinear interactions facilitate the formation of localized wave structures
- Potential observation of X-waves in spin-orbit coupled Bose-Einstein condensates

## Abstract

X-waves are an example of a localized wave packet solution of the homogeneous wave equation, and can potentially arise in any area of physics relating to wave phenomena, such as acoustics, electromagnetism, or quantum mechanics. They have been predicted in condensed matter systems such as atomic Bose-Einstein condensates in optical lattices, and were recently observed in exciton-polariton condensates. Here we show that polariton X-waves result from an interference between two separating wave packets that arise from the combination of a locally hyperbolic dispersion relation and nonlinear interactions. We show that similar X-wave structures could also be observed in expanding spin-orbit coupled Bose-Einstein condensates.