# Scattering for a particle interacting with a Bose gas

## TL;DR

This paper analyzes the long-term dynamics of a particle interacting with a Bose gas, demonstrating ballistic motion of the particle and convergence of the Bose gas wave function to a soliton.

## Contribution

It provides a rigorous analysis of the asymptotic behavior of a coupled ODE-Schrödinger system modeling particle-gas interactions, showing ballistic trajectories and soliton formation.

## Key findings

- Particle exhibits ballistic trajectory asymptotically.
- Wave function converges to a soliton in $L^{
abla}$.
- Provides insights into long-term dynamics of particle-gas systems.

## Abstract

We study the asymptotic behavior of solutions to an ODE - Schr\"{o}dinger type system that models the interaction of a particle with a Bose gas. We show that the particle has a ballistic trajectory asymptotically, and that the wave function describing the Bose gas converges to a soliton in $L^{\infty}.$