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

On explicit soliton solutions and blow-up for coupled variable coefficient nonlinear Schr\"{o}dinger equations