Constructing completely integrable fields by a generalized-streamlines method

TL;DR

This paper introduces a generalized-streamlines method to construct completely integrable fields, providing explicit solutions for complex systems like extremal surfaces in Minkowski space and Born-Infeld models.

Contribution

It develops a novel generalized-streamlines approach that yields explicit solutions for a broad class of integrable systems, extending classical flow visualization techniques.

Findings

Explicit solutions for extremal surfaces in Minkowski space

Solutions for Born-Infeld models

A new topological/soft-analytic framework for integrable systems

Abstract

The classical approach to visualizing a flow, in terms of its streamlines, motivates a topological/soft-analytic argument for constrained variational equations. In its full generality, that argument provides an explicit formula for completely integrable solutions to a broad class of n-dimensional quasilinear exterior systems. In particular, it yields explicit solutions for extremal surfaces in Minkowski space and for Born--Infeld models.