The evolution of a curve induced by the Pohlmeyer-Lund-Regge equation
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916814228815872 |
|---|---|
| author | Kobayashi, Shimpei Kogo, Yuhei Matsuura, Nozomu |
| author_facet | Kobayashi, Shimpei Kogo, Yuhei Matsuura, Nozomu |
| contents | This paper investigates the evolution of space curves governed by the Pohlmeyer-Lund-Regge (PLR) equation, an integrable extension of the sine-Gordon equation. We examine a specific type of curve evolution, known as the Lund-Regge evolution, and derive its representation in the Frenet frame. We show the Frenet frame evolution aligns with the Lax system of the PLR equation and develop a construction method for curve families via the Sym formula. In conclusion, we describe the Lund-Regge evolution corresponding the Date multi-soliton solutions to the PLR equation, with illustrations of curves and surfaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_05733 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The evolution of a curve induced by the Pohlmeyer-Lund-Regge equation Kobayashi, Shimpei Kogo, Yuhei Matsuura, Nozomu Differential Geometry Exactly Solvable and Integrable Systems 53A04 (Primary) 37K10 (Secondary) This paper investigates the evolution of space curves governed by the Pohlmeyer-Lund-Regge (PLR) equation, an integrable extension of the sine-Gordon equation. We examine a specific type of curve evolution, known as the Lund-Regge evolution, and derive its representation in the Frenet frame. We show the Frenet frame evolution aligns with the Lax system of the PLR equation and develop a construction method for curve families via the Sym formula. In conclusion, we describe the Lund-Regge evolution corresponding the Date multi-soliton solutions to the PLR equation, with illustrations of curves and surfaces. |
| title | The evolution of a curve induced by the Pohlmeyer-Lund-Regge equation |
| topic | Differential Geometry Exactly Solvable and Integrable Systems 53A04 (Primary) 37K10 (Secondary) |
| url | https://arxiv.org/abs/2504.05733 |