Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914709171601408 |
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| author | Li, Shangshuai Zhang, Da-jun |
| author_facet | Li, Shangshuai Zhang, Da-jun |
| contents | The paper establishes a direct linearization scheme for the SU(2) anti-self-dual Yang-Mills (ASDYM) equation.The scheme starts from a set of linear integral equations with general measures and plane wave factors. After introducing infinite-dimensional matrices as master functions, we are able to investigate evolution relations and recurrence relations of these functions, which lead us to the unreduced ASDYM equation. It is then reduced to the ASDYM equation in the Euclidean space and two ultrahyperbolic spaces by reductions to meet the reality conditions and gauge conditions, respectively. Special solutions can be obtained by choosing suitable measures. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06055 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces Li, Shangshuai Zhang, Da-jun Exactly Solvable and Integrable Systems The paper establishes a direct linearization scheme for the SU(2) anti-self-dual Yang-Mills (ASDYM) equation.The scheme starts from a set of linear integral equations with general measures and plane wave factors. After introducing infinite-dimensional matrices as master functions, we are able to investigate evolution relations and recurrence relations of these functions, which lead us to the unreduced ASDYM equation. It is then reduced to the ASDYM equation in the Euclidean space and two ultrahyperbolic spaces by reductions to meet the reality conditions and gauge conditions, respectively. Special solutions can be obtained by choosing suitable measures. |
| title | Direct linearization of the SU(2) anti-self-dual Yang-Mills equation in various spaces |
| topic | Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2403.06055 |