# Elastic collision and molecule formation of spatiotemporal light bullets in a cubic-quintic nonlinear medium

## TL;DR

This paper investigates the behavior, stability, and interactions of 3D spatiotemporal light bullets in a cubic-quintic nonlinear medium, revealing elastic collisions, molecule formation, and complex dynamics through analytical and numerical methods.

## Contribution

It provides a comprehensive analysis of 3D light bullets' stability and collision dynamics using variational approximation and numerical simulations, highlighting new collision behaviors.

## Key findings

- Elastic collisions at high velocities
- Formation of bullet molecules at low velocities
- Indefinite expansion and destruction at intermediate velocities

## Abstract

We consider the statics and dynamics of a stable, mobile three-dimensional (3D) spatiotemporal light bullet in a cubic-quintic nonlinear medium with a focusing cubic nonlinearity above a critical value and any defocusing quintic nonlinearity. The 3D light bullet can propagate with a constant velocity in any direction. Stability of the light bullet under a small perturbation is established numerically.We consider frontal collision between two light bullets with different relative velocities. At large velocities the collision is elastic with the bullets emerge after collision with practically no distortion. At small velocities two bullets coalesce to form a bullet molecule. At a small range of intermediate velocities the localized bullets could form a single entity which expands indefinitely leading to a destruction of the bullets after collision. The present study is based on an analytic Lagrange variational approximation and a full numerical solution of the 3D nonlinear Schr\"odinger equation.