Localized wave solutions to the vector nonlinear Schrödinger equation with nonzero backgrounds

Abstract

The vector nonlinear Schrödinger (NLS) system is studied through the generalized Darboux transformation (DT). We begin with the nonzero seed solution in the exponential form of evolution variable and explore the eigenfunction of the ‐component NLS equation. With the formulae of the eigenfunction, localized wave solutions of the two‐component and three‐component NLS equations are studied. By choosing different free parameters, some special solutions and the dynamic evolutions are presented, including breather–rogue wave, breather fission, breather fusion, and breather–soliton.