# Stable three-dimensional modon soliton in plasmas

## TL;DR

This paper derives a 3D nonlinear plasma wave equation, finds an exact soliton solution, and demonstrates through simulations that these solitons can collide elastically, advancing understanding of plasma wave dynamics.

## Contribution

It introduces a 3D generalization of the Hasegawa-Mima equation and provides an exact soliton solution with analysis of collision behavior.

## Key findings

- Exact 3D soliton solution found
- Collisions between solitons are elastic
- Provides a new model for 3D plasma wave interactions

## Abstract

We derive the nonlinear equations that describe coupled drift waves and ion acoustic waves in a plasma. We show that when the coupling to ion acoustic waves is negligible, the reduced nonlinear equation is a generalization of the Hasegawa-Mima equation to the three-dimensional (3D) case. We find an exact analytical solution of this equation in the form 3D soliton drift wave (3D modon). By numerical simulations we study collisions between the modons and show that the collisions can be fully elastic.