Conservation laws, Darboux transformation and localized waves for the [formula omitted]-coupled nonautonomous Gross–Pitaevskii equations in the Bose–Einstein condensates

Abstract

Under investigation in this paper is the N-coupled nonautonomous Gross–Pitaevskii equations, which describe the dynamics of the Bose–Einstein condensates. Based on the Lax pair, infinitely-many conservation laws and Mth-fold Darboux transformation are constructed. Three types of the nonautonomous localized waves are obtained via the Darboux transformation. The nonautonomous bound-state soliton is observed. The profile and energy distribution of the nonautonomous breather and rogue wave are shown. The influences of coefficients for the shape and position of background wave are discussed. In addition, the interactions between three types of the nonautonomous localized waves are analyzed graphically.