An integrable generalization of the Fokas-Lenells equation: Darboux transformation, reduction and explicit soliton solutions

doi:10.1088/1674-1056/ad4633

中国物理B ›› 2024, Vol. 33 ›› Issue (7): 70202-070202.doi: 10.1088/1674-1056/ad4633

An integrable generalization of the Fokas-Lenells equation: Darboux transformation, reduction and explicit soliton solutions

Jiao Wei(魏姣)¹, Xianguo Geng(耿献国)¹, and Xin Wang(王鑫)^2,†

1 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;
2 School of Mathematics and Information Science, Zhongyuan University of Technology, Zhengzhou 450007, China

收稿日期:2024-03-30 修回日期:2024-04-28 接受日期:2024-05-02 出版日期:2024-06-18 发布日期:2024-06-20
通讯作者: Xin Wang E-mail:wangxinlinzhou@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12326305, 11931017, and 12271490), the Excellent Youth Science Fund Project of Henan Province (Grant No. 242300421158), the Natural Science Foundation of Henan Province (Grant No. 232300420119), the Excellent Science and Technology Innovation Talent Support Program of ZUT (Grant No. K2023YXRC06), and Funding for the Enhancement Program of Advantageous Discipline Strength of ZUT (2022).

An integrable generalization of the Fokas-Lenells equation: Darboux transformation, reduction and explicit soliton solutions

Jiao Wei(魏姣)¹, Xianguo Geng(耿献国)¹, and Xin Wang(王鑫)^2,†

1 School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;
2 School of Mathematics and Information Science, Zhongyuan University of Technology, Zhengzhou 450007, China

Received:2024-03-30 Revised:2024-04-28 Accepted:2024-05-02 Online:2024-06-18 Published:2024-06-20
Contact: Xin Wang E-mail:wangxinlinzhou@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 12326305, 11931017, and 12271490), the Excellent Youth Science Fund Project of Henan Province (Grant No. 242300421158), the Natural Science Foundation of Henan Province (Grant No. 232300420119), the Excellent Science and Technology Innovation Talent Support Program of ZUT (Grant No. K2023YXRC06), and Funding for the Enhancement Program of Advantageous Discipline Strength of ZUT (2022).

摘要/Abstract

摘要： Under investigation is an integrable generalization of the Fokas-Lenells equation, which can be derived from the negative power flow of a $2\times 2$ matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas-Lenells system is constructed. As a reduction, the $N$-fold Darboux transformation for the generalized Fokas-Lenells equation is obtained, from which the $N$-soliton solution in a compact Vandermonde-like determinant form is given. Particularly, the explicit one- and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

关键词: Darboux transformation, soliton solutions, generalized Fokas-Lenells equation

Abstract: Under investigation is an integrable generalization of the Fokas-Lenells equation, which can be derived from the negative power flow of a $2\times 2$ matrix spectral problem with three potentials. Based on the gauge transformation of the matrix spectral problem, one kind of Darboux transformation with multi-parameters for the three-component coupled Fokas-Lenells system is constructed. As a reduction, the $N$-fold Darboux transformation for the generalized Fokas-Lenells equation is obtained, from which the $N$-soliton solution in a compact Vandermonde-like determinant form is given. Particularly, the explicit one- and two-soliton solutions are presented and their dynamical behaviors are shown graphically.

Key words: Darboux transformation, soliton solutions, generalized Fokas-Lenells equation

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems)

Jiao Wei(魏姣), Xianguo Geng(耿献国), and Xin Wang(王鑫). An integrable generalization of the Fokas-Lenells equation: Darboux transformation, reduction and explicit soliton solutions[J]. 中国物理B, 2024, 33(7): 70202-070202.

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An integrable generalization of the Fokas-Lenells equation: Darboux transformation, reduction and explicit soliton solutions

An integrable generalization of the Fokas-Lenells equation: Darboux transformation, reduction and explicit soliton solutions

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