  This work is concerned with the study of explicit solutions for a generalized
coupled nonlinear Schr\"{o}dinger equations (NLS) system with variable
coefficients. Indeed, we show, employing similarity transformations, the
existence of Rogue wave and dark-bright soliton like-solutions for such a
generalized NLS system, provided the coefficients satisfy a Riccati system. As
a result of the multiparameter solution of the Riccati system, the nonlinear
dynamics of the solution can be controlled. Finite-time singular solutions in
the $L^{\infty}$ norm for the generalized coupled NLS system are presented
explicitly. Finally, an n-dimensional transformation between a variable
coefficient NLS coupled system and a constant coupled system coefficient is
presented. Soliton and Rogue wave solutions for this high-dimensional system
are presented as well. A Mathematica file has been prepared as supplementary
material, verifying the Riccati systems used in the construction of the
solutions.
