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

TL;DR

This paper develops a novel numerical method for approximating solutions to a complex coupled Schrödinger system with mixed nonlinearities, demonstrating its effectiveness through theoretical analysis and numerical examples.

Contribution

It introduces a non-standard numerical approach transforming the continuous system into a solvable algebraic discrete form, with proven stability and convergence.

Findings

Method effectively approximates solutions in higher dimensions

Theoretical analysis confirms stability and convergence

Numerical examples illustrate efficiency and accuracy

Abstract

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.