Degenerate and bound-state solitons of a novel Kundu-nonlinear Schr?dinger equation based on generalized Darboux transformation

In this paper, we derive a novel Kundu-nonlinear Schrodinger equation through a 2 x 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 Schrodinger 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.

Automated summary

In this paper, a novel Kundu-nonlinear Schrodinger equation is derived through a 2 x 2 matrix spectral problem, which can be used to describe phenomena in optical propagation. The determinant expression of generalized (n, N-n)-fold Darboux transformation for the Kundu-nonlinear Schrodinger equation is obtained by solving algebraic equations. Additionally, three different types of solutions are obtained through the generalized (n, N - n) -fold Darboux transformation, including soliton solutions, degenerate soliton solutions, and interaction solutions between solitons and degenerate solitons, categorized into elastic interaction and bound-state. The conditions for their generation are discussed, and the properties of these solutions are analyzed graphically.