In this paper a nonlinear coupled Schrödinger 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 and convergence. At the final step, numerical examples are provided to illustrate the efficiency of the theoretical results.

中文翻译：

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混合三次超线性薛定ding系统数值解的Lyapunov–Sylvester计算方法

本文考虑了存在立方和超线性混合幂律的非线性耦合薛定ding系统。开发了一种非标准数值方法来近似高维情况下的解。该思想在于将连续系统转化为代数拟线性动力学离散变量，从而导致广义半线性算子。接下来，研究离散代数系统的可解性，稳定性和收敛性。在最后一步，提供了数值示例来说明理论结果的效率。