Low dimensional Born-Infeld equations coupled with a collisionless matter model

TL;DR

This paper studies the coupled Born-Infeld electromagnetic equations with a collisionless matter model, specifically the Vlasov equation in a simplified phase space, transforming the system into a manageable hyperbolic form.

Contribution

It introduces a transformation and initial data assumptions that enable analysis of the coupled nonlinear equations in a reduced one-and-a-half dimensional setting.

Findings

Reduced the Born-Infeld and Vlasov system to a quasilinear hyperbolic form.

Established conditions under which the nonlinear system can be effectively analyzed.

Provided a framework for studying electromagnetic fields coupled with collisionless matter in simplified models.

Abstract

We consider the Born-Infeld nonlinear electromagnetic field equations and study its Cauchy problem in the case that the Vlasov equation is considered as a matter model. In the present paper, the Vlasov equation is considered on the so-called one and one-half dimensional phase space, and in consequence the Born-Infeld equations are reduced to a quasilinear hyperbolic system with two unknowns. A transformation is introduced in order to make the field equations easy to handle, and suitable assumptions are made on initial data so that the nonlinearity of the field is controlled.