Two kinds of rogue waves of the general nonlinear Schrödinger equation with derivative

摘要: In this letter, the designable integrability (DI) of variable coefficient derivative nonlinear Schrodinger equation (VCDNLSE) is shown by construction an explicit transformation which maps VCDNLSE to usual (DNLSE). One novel feature with DI that its coefficients can be designed artificially and analytically using transformation. What more, from rogue wave rational traveling solution DNLSE, we get two kinds waves kind has vanishing boundary condition, other non-vanishing condition. The also provides a possible way control profile in physical experiments.