Relativistic Burgers and Nonlinear Schr\"odinger Equations

TL;DR

This paper introduces relativistic versions of the Burgers and nonlinear Schrödinger equations, which reduce to the classical forms in the non-relativistic limit and maintain integrability with relativistic corrections.

Contribution

The paper constructs relativistic complex Burgers-Schrödinger and nonlinear Schrödinger equations that are integrable at all orders of relativistic corrections.

Findings

Equations reduce to classical forms in the non-relativistic limit

Equations are integrable at any order of relativistic corrections

Relativistic equations extend classical models with preserved integrability

Abstract

Relativistic complex Burgers-Schr\"odinger and Nonlinear Schr\"odinger equations are constructed. In the non-relativistic limit they reduce to the standard Burgers and NLS equations respectively and are integrable at any order of relativistic corrections.