# Localized waves in plasmas at varying magnetic field

## TL;DR

This paper investigates small amplitude ion acoustic solitary waves in plasmas with varying magnetic fields, revealing the formation of solitary and localized shock waves through a nonlinear wave equation similar to KdV-Burgers, without thermal or dissipative effects.

## Contribution

It introduces a nonlinear wave model incorporating varying magnetic fields that predicts the existence of solitary and localized shock waves in plasmas without thermal pressure or dissipation.

## Key findings

- Solitary waves radiate energy during propagation.
- Existence of small amplitude localized shock profiles.
- Properties depend on environmental parameters.

## Abstract

By considering the continuity, Navier-Stoks and Poisson's equations in a non-relativistic frame work for plasmas, we study the behavior of small amplitude ion acoustic solitary waves in plasmas under the influence of a varying magnetic field. The result is a nonlinear wave equation which complies with the KdV-Burgers (KdVB) equation, surprisingly in the absence of thermal pressure or any dissipative effects. We show that the complete set of equations, by considering the varying magnetic field, create solitary waves which radiate energy during their traveling in the medium. An interesting result is the existence of small amplitude localized shock profiles beside the solitary waves. Properties of this solitaire solution is studied by considering different values for the environmental characters.