Breathers and rogue waves on the double-periodic background for the reverse-space-time derivative nonlinear Schrödinger equation

In the present investigation, the breathers and rogue waves on the double-periodic background are successfully constructed by Darboux transformation using a plane wave seed solution. Firstly, the Darboux transformation for the reverse-space-time derivative nonlinear Schrödinger equation is constructed. Secondly, periodic solutions, breathers, double-periodic solutions, breathers on the periodic and double-periodic background are derived by n-fold Darboux transformation. Thirdly, the higher-order rogue waves on the periodic and double-periodic background are constructed by semi-degenerate Darboux transformation. In addition, the dynamic behaviors of the solutions are plotted to show some interesting new solution structures.