Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2411.18140 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866929606437634048 |
|---|---|
| author | Luan, Dongli Xue, Bo Liu, Huan |
| author_facet | Luan, Dongli Xue, Bo Liu, Huan |
| contents | We investigate the inverse scattering problem for the massive Thirring model, focusing particularly on cases where the transmission coefficient exhibits $N$ pairs of higher-order poles. Our methodology involves transforming initial data into scattering data via the direct scattering problem. Utilizing two parameter transformations, we examine the asymptotic properties of the Jost functions at both vanishing and infinite parameters, yielding two equivalent spectral problems. We subsequently devise a mapping that translates the obtained scattering data into a $2 \times 2$ matrix Riemann--Hilbert problem, incorporating several residue conditions at $N$ pairs of multiple poles. Additionally, we construct an equivalent pole-free Riemann--Hilbert problem and demonstrate the existence and uniqueness of its solution. In the reflectionless case, the $N$-multipole solutions can be reconstructed by resolving two linear algebraic systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18140 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Inverse Scattering Transform for the Massive Thirring Model: Delving into Higher-Order Pole Dynamics Luan, Dongli Xue, Bo Liu, Huan Exactly Solvable and Integrable Systems We investigate the inverse scattering problem for the massive Thirring model, focusing particularly on cases where the transmission coefficient exhibits $N$ pairs of higher-order poles. Our methodology involves transforming initial data into scattering data via the direct scattering problem. Utilizing two parameter transformations, we examine the asymptotic properties of the Jost functions at both vanishing and infinite parameters, yielding two equivalent spectral problems. We subsequently devise a mapping that translates the obtained scattering data into a $2 \times 2$ matrix Riemann--Hilbert problem, incorporating several residue conditions at $N$ pairs of multiple poles. Additionally, we construct an equivalent pole-free Riemann--Hilbert problem and demonstrate the existence and uniqueness of its solution. In the reflectionless case, the $N$-multipole solutions can be reconstructed by resolving two linear algebraic systems. |
| title | Inverse Scattering Transform for the Massive Thirring Model: Delving into Higher-Order Pole Dynamics |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2411.18140 |