Numerical solution of the Schr?dinger equations by using Delta-shaped basis functions

摘要

Numerical simulations of the nonlinear Schr?dinger equations are studied using Delta-shaped basis functions, which recently proposed by Reutskiy. Propagation of a soliton, interaction of two solitons, birth of standing and mobile solitons and bound state solutions are simulated. Some conserved quantities are computed numerically for all cases. Then we extend application of the method to solve some coupled nonlinear Schr?dinger equations. Obtained systems of ordinary differential equations are solved via the fourth- order Runge-Kutta method. Numerical solutions coincide with the exact solutions in desired machine precision and invariant quantities are conserved sensibly. Some comparisons with the methods applied in the literature are carried out.