Numerical Solution of the (2+1) Dimensional Fractional-in-Space Nonlinear Schrodinger Equation Using the Split-Step Fourier Method with Strang Splitting Technique Nazaruddin Nazaruddin, Marwan Ramli, Muhammad Ikhwan, Said Munzir, Harish A Mardi
Universitas Syiah Kuala
Abstract
The research is based on the growing need to develop advanced numerical methods for solving nonlinear partial differential equations, particularly those involving fractional derivatives, to understand and model complex physical phenomena and to design innovative technologies and systems. This study investigates the numerical solution of the Fractional-in-Space Nonlinear Schrodinger (FiSNLS) equation in (2 \(+\) 1) dimensions using the split-step Fourier method with the Strang splitting technique. The results show that the FiSNLS solutions are significantly influenced by the potential trap V and the parameter attenuation \( \alpha \). For \( V=0 \), there is no potential barrier that prevents the soliton from maintaining its original shape. However, for \(V\neq0\), the FiSNLS solutions still take the form of solitons. In contrast, for \( V=0.5(x^2+y^2), V=-0.5(x^2+y^2) \), and \( V=-0.5(x^2+y^2) \), the soliton dispersion is significant. By varying the value of \(\alpha\) to 2, e, and \(\pi\), it is observed that the value of \(\alpha\) significantly affects the pattern of dispersion of the FiSNLS solutions. The results of this study indicate that the FiSNLS solutions are significantly influenced by the potential trap V and the parameter attenuation \(\alpha\), and can be used to model nonlinear dynamics in various fields of science and engineering.
