NUMERICAL SOLUTION OF CUBIC-QUINTIC NONLINEAR SCHRÖDINGER EQUATION - Omar, KAZHEEN Hasan; Easif, Fadhil (Science Journal of University of Zakho, 2025)
This paper is devoted to investigating and comparing the variational iteration method (VIM) and the residual power series method (RPSM) for solving the cubic-quintic nonlinear Schrödinger equation (CQNLSE) initially developed to elucidate the propagation of pulses in optical fibers. Next, we use the initial conditions to get the numerical solutions of the CQNLSE. We compared the known exact solutions with the approximate results obtained using both the VIM and RPSM. The exact solution and the results from RPSM are evaluated against those from VIM. The findings demonstrated that VIM outperformed RPSM in terms of accuracy, efficiency, and ease of implementation for solving the CQNLSE. In addition, the current results are shown graphically and in the table
Keywords: Numerical solution; Cubic-Quintic Nonlinear Schrödinger equation; Residual Power Series Method; Variational Iteration Method; Lagrange multiplier