a two-dimensional boubaker polynomial expansion scheme for the numerical solution of the nonlinear schrödinger equation in (2+1) dimensions

This paper introduces an approximation method for the analytical solution of the (2+1)-dimensional nonlinear schrödinger equation in a stationary pulsed regime. the approach is based on the two-dimensional boubaker polynomials expansion scheme. exploiting the analytical solutions in three-dimensional space that correspond to stationary states akin to standing waves invariant over time, we derive the probability density function to eliminate the pulsing component. the discussion includes error analysis of the approximate solutions at zero-time plane for various separation constants (ω > 0). these results highlight the optimal accuracy of time-independent solutions, especially when the separation constant approaches zero. the findings are presented clearly and comprehensively, ensuring their validity and reliability.