Approximated solutions to Born-Infeld dynamics
arXiv:1508.01791 · doi:10.1007/JHEP02(2016)002
Abstract
The Born-Infeld equation in the plane is usefully captured in complex language. The general exact solution can be written as a combination of holomorphic and anti-holomorphic functions. However, this solution only expresses the potential in an implicit way. We rework the formulation to obtain the complex potential in an explicit way, by means of a perturbative procedure. We take care of the secular behavior common to this kind of approach, by resorting to a symmetry the equation has at the considered order of approximation. We apply the method to build approximated solutions to Born-Infeld electrodynamics. We solve for BI electromagnetic waves traveling in opposite directions. We study the propagation at interfaces, with the aim of searching for effects susceptible to experimental detection. In particular, we show that a reflected wave is produced when a wave is incident on a semi-space containing a magnetostatic field.
10 pages; changes in Section VI.B
References in corpus (6)
- Testing Born-Infeld electrodynamics in waveguides
- Testing non-linear vacuum electrodynamics with Michelson interferometry
- Exploring Born-Infeld electrodynamics using plasmas
- Born-Infeld electrostatics in the complex plane
- Convergent perturbative power series solution of the stationary Maxwell--Born--Infeld field equations with regular sources
- Born-Infeld corrections to Coulombian interactions