Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2008
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866909398676275200 |
|---|---|
| author | Aratyn, H. van de Leur, J. |
| author_facet | Aratyn, H. van de Leur, J. |
| contents | We present an explicit method to perform similarity reduction of a Riemann-Hilbert factorization problem for a homogeneous GL (N, C) loop group and use our results to find solutions to the Painleve VI equation for N=3. The tau function of the reduced hierarchy is shown to satisfy the sigma-form of the Painleve VI equation. A class of tau functions of the reduced integrable hierarchy is constructed by means of a Grassmannian formulation. These solutions provide rational solutions of the Painleve VI equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0804_0785 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach Aratyn, H. van de Leur, J. Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems 17B80, 34M55, 35Q58 We present an explicit method to perform similarity reduction of a Riemann-Hilbert factorization problem for a homogeneous GL (N, C) loop group and use our results to find solutions to the Painleve VI equation for N=3. The tau function of the reduced hierarchy is shown to satisfy the sigma-form of the Painleve VI equation. A class of tau functions of the reduced integrable hierarchy is constructed by means of a Grassmannian formulation. These solutions provide rational solutions of the Painleve VI equation. |
| title | Solutions of the Painleve VI Equation from Reduction of Integrable Hierarchy in a Grassmannian Approach |
| topic | Mathematical Physics High Energy Physics - Theory Exactly Solvable and Integrable Systems 17B80, 34M55, 35Q58 |
| url | https://arxiv.org/abs/0804.0785 |