Nonlinear Sigma Model, Zakharov-Shabat Method, and New Exact Forms of the Minimal Surfaces in $R^3$

TL;DR

This paper develops a method using the Zakharov-Shabat dressing technique to derive general formulas for exact solutions of minimal surface equations in three-dimensional space, relevant to physical applications.

Contribution

It introduces a novel application of the Zakharov-Shabat method to obtain new explicit forms of minimal surfaces in $R^3$, expanding the toolkit for solving geometric PDEs.

Findings

Derived general formulas for minimal surface solutions

Presented specific examples illustrating the method

Enhanced understanding of minimal surface solutions in physics

Abstract

General formulas for the construction of exact solutions of the equation of the minimal surface in $R^3$, which appears in various physical problems, have been derived by the Zakharov-Shabat "dressing" method. Particular examples are considered.