Abstract
In this paper, we present an explicit Darboux transformation of the generalized mixed nonlinear Schrödinger (GMNLS) equation. The compact determinant representation of the n-fold Darboux transformation of the GMNLS equation is constructed and the nth-order solution is built. We further prove that only the even-fold Darboux transformation and the even-order solution of the GMNLS equation can, respectively, be reduced to the Darboux transformation and solution of the Kundu-Eckhaus equation. Furthermore, two different kinds of explicit one-soliton solutions of the GMNLS equation are constructed and discussed.
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