http://dx.doi.org/10.1103/PhysRevE.90.033309">
 

Document Type

Journal Article

Department/Unit

Department of Mathematics

Title

Numerical solution of the nonlinear Schrödinger equation with wave operator on unbounded domains

Language

English

Abstract

© 2014 American Physical Society.In this paper, we generalize the unified approach proposed in Zhang et al. [J. Zhang, Z. Xu, and X. Wu, Phys. Rev. E 78, 026709 (2008)PLEEE81539-375510.1103/PhysRevE.78.026709] to design the nonlinear local absorbing boundary conditions (LABCs) for the nonlinear Schrödinger equation with wave operator on unbounded domains. In fact, based on the methodology underlying the unified approach, we first split the original equation into two parts - the linear equation and the nonlinear equation - then achieve a one-way operator to approximate the linear equation to make the wave outgoing, and finally combine the one-way operator with the nonlinear equation to achieve the nonlinear LABCs. The stability of the equation with the nonlinear LABCs is also analyzed by introducing some auxiliary variables, and some numerical examples are presented to verify the accuracy and effectiveness of our proposed method.

Publication Date

2014

Source Publication Title

Physical Review E

Volume

90

Issue

3

Start Page

33309

Publisher

American Physical Society

ISSN (print)

15393755

ISSN (electronic)

15502376

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