Controllable vector soliton in (2+1)-dimensional coupled nonlinear Schrödinger equations with varying coefficients

In this paper, we investigate the (2+1)- dimensional coupled nonlinear Schrödinger equations with variable coefficients which are used to describe the propagation of beams in inhomogeneous and nonlinear birefringent fibers, taking into account the components in the two polarized directions. To tackle this problem, we employ the Hirota bilinear method. Multiple solitons, rogue waves, breather waves and their interaction solutions relating to the suitable choice of time-dependent coefficients are obtained. Through manipulating the relevant parameters, the propagation control and evolution are investigated for them. Several interesting transition phenomena are revealed, such as, the transitions from the bright soliton to breather, from bright rogue to periodic humps of rogue wave structures overlay on the one- and two-peak bright soliton and from the plane wave background to the periodic ones.