A remark on the algebraic normal form method applied to the Dirac-Klein-Gordon system in two space dimensions

TL;DR

This paper proves that solutions to the two-dimensional Dirac-Klein-Gordon system become free solutions over time under certain conditions, using the algebraic normal form method.

Contribution

It demonstrates the asymptotic freedom of solutions for the Dirac-Klein-Gordon system in two dimensions under non-resonance conditions, employing the algebraic normal form approach.

Findings

Solutions are asymptotically free for small initial data.

The Dirac component tends to a free Dirac solution.

The algebraic normal form method is effective for this analysis.

Abstract

We consider the massive Dirac-Klein-Gordon system in two space dimensions. Under the non-resonace mass condition, we show that the solution is asymptotically free if the initial data are sufficiently small in a suitable weighted Sobolev space. In particular, it turns out that the Dirac component of the DKG system tends to a solution of the free Dirac equation. Our proof is based on the algebraic normal form method.