Transformações de Bäcklund e equações diferenciais que descrevem superfícies pseudoesféricas - Garrido, Gabriel de Azevedo (Universidade Federal de São Carlos, 2025)
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.
Bäcklund transformations and differential equations describing pseudospherical surfaces
Keywords: Geometria diferencial; Equações diferenciais; Superfícies pseudoesféricas; Transformações de Bäcklund e Teorema de Permutabilidade de Bianchi; Differential geometry; Differential equations; Pseudospherical Surfaces; Bäcklund Transformation and Bianchi’s Permutability Theorem; CIENCIAS EXATAS E DA TERRA::MATEMATICA::GEOMETRIA E TOPOLOGIA::GEOMETRIA DIFERENCIAL; 4. Educação de Qualidade