A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

doi:10.1088/1674-1056/20/3/030204

Abstract This paper considers the one-dimensional dissipative cubic nonlinear Schrödinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.

Keywords: dissipative cubic nonlinear Schrödinger equation three-level finite difference convergence and stability analysis

Received: 11 March 2010
Revised: 22 October 2010
Accepted manuscript online:

PACS:

02.60.-x

(Numerical approximation and analysis)

Cite this article:

Zhang Rong-Pei(张荣培),Yu Xi-Jun(蔚喜军),and Zhao Guo-Zhong(赵国忠) A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation 2011 Chin. Phys. B 20 030204

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A new finite difference scheme for a dissipative cubic nonlinear Schr"odinger equation

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