Author(s)

Khadijah Alamoudi, Mohmmad Said Hammoudeh

Department of Math, King Abdulaziz University, Jeddah, Saudi Arabia.

Models of the coupled nonlinear Schrödinger equations submit various critical physical phenomena with a typical equation for optical fibres with linear refraction. In this article, we will presuppose the Compact Finite Difference method with Runge-Kutta of order 4 (explicit) method, which is sixth-order and fourth-order in space and time respectively, to solve coupled nonlinear Schrödinger equations. Many methods used to solve coupled nonlinear Schrödinger equations are second order in time and need to use extra-technique to rise up to fourth-order as Richardson Extrapolation technique. The scheme obtained is immediately fourth-order in one step. This approach is a conditionally stable method. The conserved quantities and the exact single soliton solution indicate the competence and accuracy of the article’s suggestion schemes. Furthermore, the article discusses the two solitons interaction dynamics.

Coupled Nonlinear Schrodinger Equations, Sixth Order Method, Interaction of Two Solitons, Compact Finite Difference, Runge-Kutta of Order 4 Method

Alamoudi, K. and Hammoudeh, M. (2021) Explicit High-Order Method to Solve Coupled Nonlinear Schrödinger Equations. Advances in Pure Mathematics, 11, 472-482. doi: 10.4236/apm.2021.115033.