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

作　　者：魏姣 耿献国 王鑫 Jiao Wei;Xianguo Geng;and Xin Wang(School of Mathematics and Statistics,Zhengzhou University,Zhengzhou 450001,China;School of Mathematics and Information Science,Zhongyuan University of Technology,Zhengzhou 450007,China)

机构地区：[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

出　　处：《Chinese Physics B》2024年第7期117-124,共8页中国物理B（英文版）

基　　金：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);Funding for the Enhancement Program of Advantageous Discipline Strength of ZUT(2022)。

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 × 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 

分 类 号：O175.29[理学—数学]