A Lax Representation for the Born-Infeld Equation

TL;DR

This paper explores the Born-Infeld equation using a Lagrangian approach, revealing a novel dispersionless Lax representation that uncovers all conserved charges and highlights the system's duality symmetry.

Contribution

It introduces a dispersionless nonstandard Lax representation for the Born-Infeld equation, enabling the derivation of all conserved charges and emphasizing duality symmetry.

Findings

Derived Hamiltonian from the Lagrangian formulation.

Established a dispersionless Lax representation for the system.

Generated all conserved charges, including previously unknown ones.

Abstract

We study the Born-Infeld equation from a Lagrangian point of view emphasizing the duality symmetry present in such systems. We obtain the Hamiltonian formulation directly from the Lagrangian. We also show that this system admits a dispersionless nonstandard Lax representation which directly leads to all the conserved charges (including the ones not previously obtained). We also present the generating function for these charges and point out various other properties of this system.