# Steen-Ermakov-Pinney equation and integrable nonlinear deformation of one-dimensional Dirac equation

## TL;DR

This paper explores a nonlinear deformation of the one-dimensional Dirac equation, utilizing the Steen-Ermakov-Pinney equation to analyze invariants and establish equivalence with a linear Dirac equation.

## Contribution

It introduces a novel approach to nonlinear deformation of the Dirac equation using the Steen-Ermakov-Pinney framework, linking invariants to linear equations.

## Key findings

- Identification of invariants for the nonlinear Dirac equation
- Equivalence established between nonlinear and linear Dirac equations based on invariants
- New method for analyzing nonlinear deformations of fundamental equations

## Abstract

The paper deals with nonlinear one-dimensional Dirac equation. We describe its invariants set by means of the deformed linear Dirac equation, using the fact that two ordinary differential equations are equivalent if their sets of invariants coincide.