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Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation

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Abstract

We consider the periodic standing waves in the derivative nonlinear Schrödinger (DNLS) equation arising in plasma physics. By using a newly developed algebraic method with two eigenvalues, we classify all periodic standing waves in terms of eight eigenvalues of the Kaup–Newell spectral problem located at the end points of the spectral bands outside the real line. The analytical work is complemented with the numerical approximation of the spectral bands, this enables us to fully characterize the modulational instability of the periodic standing waves in the DNLS equation.

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Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (No. 11971103).

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Authors and Affiliations

  1. School of Mathematics, Southeast University, Nanjing, Jiangsu, 210096, People’s Republic of China

    Jinbing Chen

  2. Department of Mathematics, McMaster University, Hamilton, Ontario, L8S 4K1, Canada

    Dmitry E. Pelinovsky

  3. Department of Applied Mathematics, University of Washington, Seattle, WA, 98195, USA

    Jeremy Upsal

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  1. Jinbing Chen
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  2. Dmitry E. Pelinovsky
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  3. Jeremy Upsal
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Correspondence to Dmitry E. Pelinovsky.

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Communicated by Peter Miller.

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Chen, J., Pelinovsky, D.E. & Upsal, J. Modulational Instability of Periodic Standing Waves in the Derivative NLS Equation. J Nonlinear Sci 31, 58 (2021). https://doi.org/10.1007/s00332-021-09713-5

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  • DOI: https://doi.org/10.1007/s00332-021-09713-5

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