On the Bj\"orling problem for Born-Infeld solitons

TL;DR

This paper explores the Bj"orling problem for Born-Infeld solitons, extending classical minimal surface solutions to a physics-related nonlinear equation, and provides representation formulas for these surfaces.

Contribution

It introduces the Bj"orling problem for Born-Infeld solitons and develops solution methods and representation formulas for these surfaces.

Findings

Solutions for locally Born-Infeld soliton surfaces

Representation formulas for Born-Infeld soliton surfaces

Extension to graph-like surfaces

Abstract

The Bj\"orling problem and its solution is a well known result for minimal surfaces in Euclidean three-space. The minimal surface equation is similar to the Born-Infeld equation, which is naturally studied in physics. In this semi-expository article, we ask the question of the Bj\"orling problem for Born-Infeld solitons. This begins with the case of locally Born-Infeld soliton surfaces and later moves on to graph-like surfaces. We also present some results about their representation formulae.