Fokas–Lenells equation: Three types of Darboux transformation and multi-soliton solutions. (September 2020) - Wang, Yao; Xiong, Zhi-Jin; Ling, Liming
Abstract: In this letter, we report two novel Lax pairs for the Fokas–Lenells equation by the gauge transformation. Based on this result, we construct the three Darboux transformations and prove that they are equivalent to each other. Then we utilize the Darboux transformation to generate the multi-soliton solutions, some of which are exhibited explicitly to illustrate the distinct properties of Fokas–Lenells equation.