Transformações de Bäcklund e equações diferenciais que descrevem superfícies pseudoesféricas

Abstract

In this work, we will study Bäcklund transformations and differential equations which describe pseudospherical surfaces, focusing on the sine-Gordon equation. We also use Bianchi’s Permutability Theorem to generate new solutions and parameterize the surfaces derived from the solutions of the aforementioned equation. Some of these surfaces are presented at the end of the text.