Generalized Darboux transformation and rational soliton solutions for Chen–Lee–Liu equation

In this paper, the Chen–Lee–Liu (C–L–L) equation is investigated by the Darboux transformation (DT) method. A specific construction of the N-fold DT for C–L–L equation is derived in a simple way. The form of the N-fold DT is a matrix polynomial and each element of the matrix can be expressed by a ratio of two determinants. Furthermore, by choosing suitable eigenvalues and eigenfunctions under the reduction conditions, we can obtain the determinant solution of the reduced C–L–L equation. Moreover, the generalized DT (gDT) for C–L–L equation is also constructed through the limiting technique. As applications of the gDT method, the first and the second-order rational solitons with vanished background (VBC) and non-vanished background (NVBC) from different seeds are calculated for C–L–L equation. We hope our results can be realized by experiments in plasma physics and optical fibers.