中国物理B ›› 2024, Vol. 33 ›› Issue (7): 70202-070202.doi: 10.1088/1674-1056/ad4633
Jiao Wei(魏姣)1, Xianguo Geng(耿献国)1, and Xin Wang(王鑫)2,†
Jiao Wei(魏姣)1, Xianguo Geng(耿献国)1, and Xin Wang(王鑫)2,†
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.
中图分类号: (Partial differential equations)