Qualitative aspects of equations describing pseudospherical surfaces
Geometric and qualitative aspects of some non-local integrable models
| Full text | |
| Author(s): |
da Silva, Priscila Leal
;
Freire, Igor Leite
;
Filho, Nazime Sales
Total Authors: 3
|
| Document type: | Journal article |
| Source: | Journal of Differential Equations; v. 419, p. 33-pg., 2025-02-25. |
| Abstract | |
We study an integrable equation whose solutions define a triad of one-forms describing a surface with Gaussian curvature -1. We identify a local group of diffeomorphisms that preserve these solutions and establish conserved quantities. From the symmetries, we obtain invariant solutions that provide explicit metrics for the surfaces. These solutions are unbounded and often appear in mirrored pairs. We introduce the "collage" method, which uses conserved quantities to remove unbounded parts and smoothly join the solutions, leading to weak solutions consistent with the conserved quantities. As a result we get pseudo-peakons, which are smoother than Camassa-Holm peakons. Additionally, we apply a Miura-type transformation to relate our equation to the Degasperis-Procesi equation, allowing us to recover peakon and shock-peakon solutions for it from the solutions of the other equation. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies. (AU) | |
| FAPESP's process: | 24/01437-8 - Qualitative aspects of equations describing pseudospherical surfaces |
| Grantee: | Igor Leite Freire |
| Support Opportunities: | Regular Research Grants |