Large time behavior of solution to nonlinear Dirac equation in $1+1$ dimensions

TL;DR

This paper investigates the long-term behavior of solutions to a class of nonlinear massless Dirac equations in 1+1 dimensions, demonstrating convergence to traveling wave solutions as time approaches infinity.

Contribution

It provides a rigorous analysis of the asymptotic behavior of nonlinear Dirac equations in low dimensions, showing solutions tend to traveling waves over time.

Findings

Solutions tend to traveling wave solutions as time goes to infinity

The study characterizes the large time asymptotics of nonlinear Dirac equations in 1+1 dimensions

The results contribute to understanding wave propagation in relativistic quantum models

Abstract

This paper studies the large time behavior of solution for a class of nonlinear massless Dirac equations in $R^{1+1}$. It is shown that the solution will tend to travelling wave solution when time tends to infinity.