Exact quasi-periodic solutions to the MKdV equation
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866909713667457024 |
|---|---|
| author | Bernatska, Julia |
| author_facet | Bernatska, Julia |
| contents | In the present paper, a hierarchy of the mKdV equation is integrated by the methods of algebraic geometry. The mKdV hierarchy in question arises on coadjoint orbits in the loop algebra of $\mathfrak{sl}(2)$, and employs a family of hyperelliptic curves as spectral curves. A generic form of the finite-gap solution in any genus is obtained in terms of the $\wp$-functions, which generalize the Weierstrass $\wp$-function. Reality conditions for quasi-periodic wave solutions are completely specified. The obtained solutions are illustrated by plots in small genera. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_23469 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Exact quasi-periodic solutions to the MKdV equation Bernatska, Julia Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry 37J35, 37J37, 37J38 In the present paper, a hierarchy of the mKdV equation is integrated by the methods of algebraic geometry. The mKdV hierarchy in question arises on coadjoint orbits in the loop algebra of $\mathfrak{sl}(2)$, and employs a family of hyperelliptic curves as spectral curves. A generic form of the finite-gap solution in any genus is obtained in terms of the $\wp$-functions, which generalize the Weierstrass $\wp$-function. Reality conditions for quasi-periodic wave solutions are completely specified. The obtained solutions are illustrated by plots in small genera. |
| title | Exact quasi-periodic solutions to the MKdV equation |
| topic | Exactly Solvable and Integrable Systems Mathematical Physics Algebraic Geometry 37J35, 37J37, 37J38 |
| url | https://arxiv.org/abs/2507.23469 |