The nth-Darboux Transformation and Explicit Solutions of the PT-Symmetry Second-Type Derivative Nonlinear Schrodinger Equation

Non-local problems have become one of the research hotspots in recent years since Ablowitz-Musslimani constructed an integrable non-local nonlinear Schrodinger (NLS) equation in 2013. In this paper, we first derive the PT-symmetry second derivative nonlinear Schrodinger (PT-DNLSII) equation. Then we present the nth-Darboux transformation (DT) of the PT-DNLSII equation. As applications, starting from the zero seed solution and non-zero periodic seed solution, the explicit expressions of the multi-soliton solutions, bright soliton solution, dark soliton solution and breather soliton solution of the PT-DNLSII equation are worked out.

Automated summary

Non-local problems and integrable non-local nonlinear Schrödinger equation have attracted significant research attention. In this paper, we derive the PT-symmetry second derivative nonlinear Schrödinger equation and present the nth-Darboux transformation of the equation. We also provide explicit expressions for various soliton solutions of the PT-DNLSII equation.