# Dissipative nonlinear waves in a gravitating quantum fluid

## TL;DR

This paper analyzes nonlinear wave behavior in a dissipative, self-gravitating Bose-Einstein condensate, revealing how dissipation affects wave stability and soliton dynamics within a quantum fluid influenced by gravity.

## Contribution

It provides an analytical study of wave propagation in a dissipative, self-gravitating quantum fluid using the Gross-Pitaevskii model, deriving a modified KdV equation and analyzing soliton decay.

## Key findings

- Dissipation suppresses dynamical instabilities.
- Soliton energy, amplitude, and velocity decay over time.
- Soliton width increases, leading to finite lifetime.

## Abstract

Nonlinear wave propagation is studied analytically in a dissipative, self-gravitating Bose Einstein condensate, in the framework of Gross-Pitaevskii model. The linear dispersion relation shows that the effect of dissipation is to suppress dynamical instabilities that destabilize the system. The small amplitude analysis using reductive perturbation technique is found to yield a modified form of KdV equation. The soliton energy, amplitude and velocity are found to decay with time, whereas the soliton width increases, such that the soliton exists for a finite time only