On a mixed cubic-superlinear non radially symmetric Schrödinger system - Part II: Numerical solutions
This work provides a numerical approach for a specific class of Schrödinger systems, but the results are incremental and domain-specific.
The paper develops a numerical method for a nonlinear coupled Schrödinger system with mixed cubic and superlinear power laws, proving solvability, stability, and convergence, and demonstrating efficiency with numerical examples.
In this paper a nonlinear coupled Schrodinger system in the presence of mixed cubic and superlinear power laws is considered. A non standard numerical method is developed to approximate the solutions in higher dimensional case. The idea consists in transforming the continuous system into an algebraic quasi linear dynamical discrete one leading to generalized semi-linear operators. Next, the discrete algebraic system is studied for solvability, stability, convergence and stability. At the final step, numerical examples are provided to illustrate the efficiency of the theoretical results.