Rational solutions of Painlevé-II equation as Gram determinant

doi:10.1088/1674-1056/ad01a5

中国物理B ›› 2023, Vol. 32 ›› Issue (12): 120205-120205.doi: 10.1088/1674-1056/ad01a5

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

收稿日期:2023-08-30 修回日期:2023-09-08 接受日期:2023-10-10 出版日期:2023-11-14 发布日期:2023-11-22
通讯作者: Xiaoen Zhang E-mail:xezhang19890309@163.com
基金资助:
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).

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

Received:2023-08-30 Revised:2023-09-08 Accepted:2023-10-10 Online:2023-11-14 Published:2023-11-22
Contact: Xiaoen Zhang E-mail:xezhang19890309@163.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Painlevé-II equation, Darboux transformation, rational solutions

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.

Key words: Painlevé-II equation, Darboux transformation, rational solutions

中图分类号: (Integrable systems)

02.30.Ik

04.20.Jb (Exact solutions) 02.60.Cb (Numerical simulation; solution of equations)

Xiaoen Zhang(张晓恩) and Bing-Ying Lu(陆冰滢). Rational solutions of Painlevé-II equation as Gram determinant[J]. 中国物理B, 2023, 32(12): 120205-120205.

Xiaoen Zhang(张晓恩) and Bing-Ying Lu(陆冰滢). Rational solutions of Painlevé-II equation as Gram determinant[J]. Chin. Phys. B, 2023, 32(12): 120205-120205.

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Rational solutions of Painlevé-II equation as Gram determinant

Rational solutions of Painlevé-II equation as Gram determinant

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