Study of Homotopy Perturbation Transform for Solving Cubic-Quintic Nonlinear Schrödinger Equation

This paper is devoted to investigating and comparing the homotopy perturbation method and the homotopy perturbation transform method for solving the cubic quintic nonlinear Schrödinger equation. Both proposed methods are iterative schemes to find solutions without discretization, linearization, or restrictive assumptions. The solutions obtained in this research are approximate analytical series solutions to the cubic-quintic nonlinear Schrödinger equation. Using the homotopy perturbation method and the homotopy perturbation transform method. These methods generate rapidly converging series that approximate the behavior of the wave function over time. In addition, the current results have been shown graphically and in a table. The results demonstrate that the homotopy perturbation transform method provides more accurate and efficient solutions than the standard homotopy perturbation method.