Approximate Numerical Solutions of the Sasa-Satsuma Equation Using Residual Power Series and Perturbation Techniques

This research employs the homotopy perturbation method, the homotopy perturbation transform method, and the residual power series method to address one of the nonlinear Schrödinger equations, specifically the Sasa-Satsuma equation. The homotopy perturbation method, the homotopy perturbation transform method, and the residual power series method are powerful semi-analytical methods for solving nonlinear problems, each providing reliable and accurate approximate solutions. The approximated solutions obtained via three numerical schemes are compared with the exact solution. To illustrate the efficacy and applicability of these techniques, the current results have been shown graphically and in a table. The results showed that the homotopy perturbation transform method and the residual power series method are more effective for implementing the Sasa-Satsuma equation than the homotopy perturbation method.