an:05245541
Zbl 1133.65063
Ismail, M. S.
A fourth-order explicit schemes for the coupled nonlinear Schr??dinger equation
EN
Appl. Math. Comput. 196, No. 1, 273-284 (2008).
00215899
2008
j
65M06 35Q55 65M20 65L06
coupled nonlinear Schr??dinger equation; Runge-Kutta method; interaction of two solitons; finite difference method; semidiscretization; numerical examples; comparison of methods
Summary: We derive numerical methods for solving the coupled nonlinear Schr??dinger equation. We discretize the space derivative by central difference formulas of fourth-order. The resulting ordinary differential system is solved by the fourth-order explicit Runge-Kutta method. Neumann and periodic boundary conditions are used. The method is tested for accuracy and the conserved quantities. These methods conserve the three conserved quantities exactly for at least five decimal places. A comparison has been made with some existing methods.