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

Salih, Knier Adil; Manaa, Saad

doi:10.24271/psr.2025.522679.2138

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

Document Type : Original Article

Authors

Knier Adil Salih

Saad Manaa

Department of Mathematics, College of Science, University of Zakho, Zakho 42002, Dohuk, Iraq.

10.24271/psr.2025.522679.2138

Abstract

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.

Keywords

Homotopy perturbation method

Laplace transform

He's polynomial

Residual power series method