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Spatial frequency range analysis for the nonlinear Schrödinger equation

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Abstract

An analysis of the spatial frequency ranges for the nonlinear Schrödinger equation (NLS), subject to initial conditions with Gaussian and band-limited spatial frequency spectra, is presented in this paper. The analysis is based on a Volterra series representation of the NLS equation. This study reveals the relationship between the spatial frequency ranges of the solution, along with the evolution of the system, and the spatial frequency ranges of the initial conditions, and extends previous results in linear and nonlinear finite dimensional systems. The analysis also reveals a variety of nonlinear phenomena including self-phase modulation, cross-phase modulation and Raman effects modelled using the NLS equation.

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Acknowledgments

The authors gratefully acknowledge support from the UK Engineering and Physical Sciences Research Council (EPSRC) and the European Research Council (ERC).

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Authors and Affiliations

  1. Department of Automatic Control and Systems Engineering, The University of Sheffield, Sheffield, S1 3JD, UK

    L. Z. Guo, Y. Z. Guo, S. A. Billings, D. Coca & Z. Q. Lang

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  1. L. Z. Guo
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  2. Y. Z. Guo
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  3. S. A. Billings
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  4. D. Coca
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  5. Z. Q. Lang
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Correspondence to L. Z. Guo.

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Guo, L.Z., Guo, Y.Z., Billings, S.A. et al. Spatial frequency range analysis for the nonlinear Schrödinger equation. Nonlinear Dyn 78, 93–102 (2014). https://doi.org/10.1007/s11071-014-1423-0

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  • DOI: https://doi.org/10.1007/s11071-014-1423-0

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