Abstract
In this paper, we derive a novel Kundu-nonlinear Schrödinger equation through a 2 × 2 matrix spectral problem, which can be used to describe the phenomena in optical propagation, and the determinant expression of generalized (n,N−n)-fold Darboux transformation for the Kundu-nonlinear Schrödinger equation is given by solving algebraic equations. In addition, through the generalized (n,N−n)-fold Darboux transformation, we obtain three different types of solutions, (i) soliton solutions, (ii) degenerate soliton solutions, (iii) interaction solutions between solitons and degenerate solitons, which are divided into elastic interaction and bound-state. At the same time, the conditions for their generation are discussed. The properties of the aforementioned solutions are analyzed graphically ultimately.
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