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Rational solutions of Painlevé-II equation as Gram determinant |
| Xiaoen Zhang(张晓恩)1,† and Bing-Ying Lu(陆冰滢)2 |
1 College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China;
2 SISSA, Via Bonomea 265, Trieste, Italy |
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Abstract Under the Flaschka-Newell Lax pair, the Darboux transformation for the Painlevé-II equation is constructed by the limiting technique. With the aid of the Darboux transformation, the rational solutions are represented by the Gram determinant, and then we give the large y asymptotics of the determinant and the rational solutions. Finally, the solution of the corresponding Riemann-Hilbert problem is obtained from the Darboux matrices.
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Received: 30 August 2023
Revised: 08 September 2023
Accepted manuscript online: 10 October 2023
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PACS:
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02.30.Ik
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(Integrable systems)
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04.20.Jb
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(Exact solutions)
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02.60.Cb
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(Numerical simulation; solution of equations)
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| Fund: The authors sincerely thank Professor Liming Ling for his guidance and help. Project supported by the National Natural Science Foundation of China (Grant No.12101246). |
Corresponding Authors:
Xiaoen Zhang
E-mail: xezhang19890309@163.com
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Cite this article:
Xiaoen Zhang(张晓恩) and Bing-Ying Lu(陆冰滢) Rational solutions of Painlevé-II equation as Gram determinant 2023 Chin. Phys. B 32 120205
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