# Born-Infeld solitons, Maximal surfaces and Ramanujan's identities

## TL;DR

This paper explores the connections between Born-Infeld solitons, maximal surfaces, and Ramanujan's identities, providing new solutions, methods for constructing complex solitons, and deriving novel mathematical identities.

## Contribution

It introduces a method to generate complex solitons from maximal surfaces and links these to Ramanujan's identities using the Weierstrass-Enneper representation.

## Key findings

- Exact solutions of the Born-Infeld equation from maximal surface solutions
- A new method to construct complex solitons from maximal surfaces
- Derivation of new mathematical identities using Ramanujan's identities

## Abstract

We show that a Born-Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. We also obtain some exact solutions of the Born-Infeld equation from already known solutions to the maximal surface equation. Further we present a method to construct a one-parameter family of complex solitons from a given one parameter family of maximal surfaces. Finally, using Ramanujan's Identities and the Weierstrass-Enneper representation of maximal surfaces, we derive further non-trivial identities.