Numerical solution of the nonlinear Schrödinger equation with wave operator on unbounded domains
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)] to design the nonlinear local absorbing boundary conditions (LABCs) for the nonlinear Schrödinger equation with wave operator on unbounded domains. In fact, based o...
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| Published in: | Physical review. E, Statistical, nonlinear, and soft matter physics Vol. 90; no. 3; p. 033309 |
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| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
United States
01.09.2014
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| Subjects: | |
| ISSN: | 1539-3755, 1550-2376, 1550-2376 |
| Online Access: | Get full text |
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| Summary: | 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)] 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. |
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| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
| ISSN: | 1539-3755 1550-2376 1550-2376 |
| DOI: | 10.1103/PhysRevE.90.033309 |