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Relay-Zone Technique for Numerical Boundary Treatments in Simulating Dark Solitons

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Abstract

To simulate dark solitons in the defocusing nonlinear Schrödinger equation, we introduce a relay-zone technique, by alternately using a Robin boundary condition to treat the nonzero far field, and a derivative boundary condition to match the dark soliton. Numerical tests and comparisons demonstrate the effectiveness of the proposed boundary treatment. Stability and interaction of dark solitons are also studied.

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Acknowledgements

The research is partially supported by NSFC under Contract no. 11521202 and China Postdoctoral Science Foundation Funded Project no. 2016M600902.

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Authors and Affiliations

  1. College of Engineering, Peking University, Beijing, 100871, People’s Republic of China

    Lei Bian & Shaoqiang Tang

  2. Beijing Computational Science Research Center, Beijing, 100193, People’s Republic of China

    Lei Bian

  3. Travelsky Mobile Technology Limited, Beijing, 100029, People’s Republic of China

    Lei Bian

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  1. Lei Bian
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  2. Shaoqiang Tang
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Correspondence to Lei Bian.

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Bian, L., Tang, S. Relay-Zone Technique for Numerical Boundary Treatments in Simulating Dark Solitons. Multiscale Sci. Eng. 1, 210–219 (2019). https://doi.org/10.1007/s42493-018-00002-0

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