New schemes for the coupled nonlinear Schrödinger equation

Abstract

In this paper, we present three new schemes for the coupled nonlinear Schrödinger equation. The three new schemes are multi-symplectic schemes that preserve the intrinsic geometry property of the equation. The three new schemes are also semi-explicit in the sense that they need not solve linear algebraic equations every time-step, which is usually the most expensive in numerical simulation of partial differential equations. Many numerical experiments on collisions of solitons are presented to show the efficiency of the new multi-symplectic schemes.

Keywords:

• coupled nonlinear Schrödinger equation
• multi-symplectic scheme
• Euler-box scheme
• solitons

2000 AMS Subject Classification :

• 65L05
• 65L70
• 70H05
• 34A50

Acknowledgements

The work was supported by National Basic Research Program under the Grant 2005CB321703, Key Project of Jiangsu NSF (No. BK2006725) and NSFC (No. 10471067 & 40405019).