On traveling wave solutions to Manakov model with variable coefficients

We use a general transformation, to find exact solutions for the Manakov system with variable coefficients (depending on the time e \varepsilon ) using an improved tanh-coth method. The solutions obtained in this work are more general compared to those in other works because they involve variable coefficients. The implemented computational method is applied in a direct way on the reduced system, avoid in this way the reduction to only one equation, as occurs in the works respect to exact solutions, made by other authors. Clearly, from the solutions obtained here, new solutions are derived for the standard model (constant coefficients), complementing in this way the results obtained by other authors mentioned here. Finally, we give some discussion on the results and give the respective conclusions.