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

doi:10.1088/1674-1056/ad4633

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.

Keywords: Darboux transformation soliton solutions generalized Fokas-Lenells equation

Received: 30 March 2024
Revised: 28 April 2024
Accepted manuscript online: 02 May 2024

PACS:	02.30.Jr	(Partial differential equations)
	02.30.Ik	(Integrable systems)

Fund: 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).

Corresponding Authors: Xin Wang
E-mail: wangxinlinzhou@163.com

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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 2024 Chin. Phys. B 33 070202

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

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