Born-Infeld Solitons and Existence & Non-uniqueness of Solutions to the Björling Problem

In this semi-expository article, we study Born-Infeld soliton surfaces as zero mean curvature surfaces and derive conformal parameters for them. Then we present two approaches to solve the Björling problem for such surfaces, one of them treating them as time-like minimal surfaces and the other one using the Barbashov-Chernikov representation. Finally, we show that the solution to the Björling problem may not be unique unlike minimal and maximal surfaces.