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Stabilization of the higher order nonlinear Schrödinger equation with constant coefficients

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Abstract

We study the internal stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. Combining multiplier techniques, a fixed point argument and nonlinear interpolation theory, we can obtain the well-posedness. Then, applying compactness arguments and a unique continuation property, we prove that the solution of the higher-order nonlinear Schrödinger equation with a damping term decays exponentially.

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Acknowledgements

The author would sincerely like to thank the referees for their interesting comments. He also thanks Prof. Yong Li for many useful suggestions and help. This work was supported by NSFC Grant (11701078), China Post-doctoral Science Foundation (2017M611292), the Fundamental Research Funds for the Central Universities (2412017QD002), NSFC Grants (11626043 and 11601073).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Center for Mathematics and Interdisciplinary Sciences, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Mo Chen

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  1. Mo Chen
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Correspondence to Mo Chen.

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Communicating Editor: S Kesavan

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Chen, M. Stabilization of the higher order nonlinear Schrödinger equation with constant coefficients. Proc Math Sci 128, 39 (2018). https://doi.org/10.1007/s12044-018-0410-7

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  • DOI: https://doi.org/10.1007/s12044-018-0410-7

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