# Weakly bound solitons and two-soliton molecules in dipolar Bose-Einstein condensates

## TL;DR

This paper derives analytic expressions for dipolar bright soliton interactions and explores weakly bound soliton molecules in dipolar Bose-Einstein condensates, combining variational methods with numerical simulations.

## Contribution

It introduces a variational approach to model the evolution of dipolar soliton molecules and compares predictions with numerical simulations, demonstrating good agreement.

## Key findings

- Analytic interaction potential for dipolar bright solitons.
- Description of weakly bound two-soliton molecules.
- Qualitative agreement between model predictions and simulations.

## Abstract

Analytic expressions have been derived for the interaction potential between dipolar bright solitons and the binding energy of a two-soliton molecule. The properties of these localized structures are explored with a focus on their behavior in the weakly bound regime, with a small binding energy. Using the variational approach a coupled system of ordinary differential equations for the parameters of a soliton molecule is obtained for the description of their evolution. Predictions of the model are compared with numerical simulations of the governing nonlocal Gross-Pitaevskii equation and good qualitative agreement between them is demonstrated.