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In this paper a nonlinear coupled Schrodinger system in the presence of mixedcubic and superlinear power laws is considered. A non standard numerical methodis developed to approximate the solutions in higher dimensional case. The ideaconsists in transforming the continuous system into an algebraic quasi lineardynamical discrete one leading to generalized semi-linear operators. Next, thediscrete algebraic system is studied for solvability, stability, convergenceand stability. At the final step, numerical examples are provided to illustratethe efficiency of the theoretical results.

On a mixed cubic-superlinear non radially symmetric Schr\"odinger system - Part II: Numerical solutions