From Algebro Geometric Solutions of the Toda Equation to Sato Formulas
We know that the degeneracy of solutions to PDEs, given in terms of theta functions on Riemann surfaces, provides important results about particular solutions, as in the case of the NLS equation. Here, we degenerate the so called finite gap solutions of the Toda lattice equation from the general for...
Saved in:
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-07-01
|
| Series: | AppliedMath |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2673-9909/4/3/46 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850259158190784512 |
|---|---|
| author | Pierre Gaillard |
| author_facet | Pierre Gaillard |
| author_sort | Pierre Gaillard |
| collection | DOAJ |
| description | We know that the degeneracy of solutions to PDEs, given in terms of theta functions on Riemann surfaces, provides important results about particular solutions, as in the case of the NLS equation. Here, we degenerate the so called finite gap solutions of the Toda lattice equation from the general formulation in terms of abelian functions when the gaps tend to points. This degeneracy allows us to recover the Sato formulas without using inverse scattering theory or geometric or representation theoretic methods. |
| format | Article |
| id | doaj-art-5988a0f274c844a5a03beb5a4b1aa74b |
| institution | OA Journals |
| issn | 2673-9909 |
| language | English |
| publishDate | 2024-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | AppliedMath |
| spelling | doaj-art-5988a0f274c844a5a03beb5a4b1aa74b2025-08-20T01:55:57ZengMDPI AGAppliedMath2673-99092024-07-014385686710.3390/appliedmath4030046From Algebro Geometric Solutions of the Toda Equation to Sato FormulasPierre Gaillard0Faculté des Sciences Mirande, Université de Bourgogne Franche-Comté, 2100 Dijon, FranceWe know that the degeneracy of solutions to PDEs, given in terms of theta functions on Riemann surfaces, provides important results about particular solutions, as in the case of the NLS equation. Here, we degenerate the so called finite gap solutions of the Toda lattice equation from the general formulation in terms of abelian functions when the gaps tend to points. This degeneracy allows us to recover the Sato formulas without using inverse scattering theory or geometric or representation theoretic methods.https://www.mdpi.com/2673-9909/4/3/46Riemann surfacestheta functionsabelian integralsBaker Akhiezer functionsSato formulas |
| spellingShingle | Pierre Gaillard From Algebro Geometric Solutions of the Toda Equation to Sato Formulas AppliedMath Riemann surfaces theta functions abelian integrals Baker Akhiezer functions Sato formulas |
| title | From Algebro Geometric Solutions of the Toda Equation to Sato Formulas |
| title_full | From Algebro Geometric Solutions of the Toda Equation to Sato Formulas |
| title_fullStr | From Algebro Geometric Solutions of the Toda Equation to Sato Formulas |
| title_full_unstemmed | From Algebro Geometric Solutions of the Toda Equation to Sato Formulas |
| title_short | From Algebro Geometric Solutions of the Toda Equation to Sato Formulas |
| title_sort | from algebro geometric solutions of the toda equation to sato formulas |
| topic | Riemann surfaces theta functions abelian integrals Baker Akhiezer functions Sato formulas |
| url | https://www.mdpi.com/2673-9909/4/3/46 |
| work_keys_str_mv | AT pierregaillard fromalgebrogeometricsolutionsofthetodaequationtosatoformulas |