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From generalized Fourier transforms to spectral curves for the Manakov hierarchy. II. Spectral curves for the Manakov hierarchy

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Abstract

The hierarchies of multicomponent models of Manakov type are briefly outlined. Many of them have important applications n nonlinear optics. Next, we develop a method for calculating the spectral curves for the multiphase solutions of these equations. We discuss also other multicomponent generalization of Manakov system to which our method can be extended.

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Acknowledgements

This work has been supported by the Bulgarian Science Foundation (Grant NTS-Russia 02/101 from 23.10.2017) and by the RFBR (Grant 18-51-18007).

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Authors and Affiliations

  1. Sankt-Petersburg State University of Aerospace Instrumentation, St-Petersburg, Russia

    A. O. Smirnov & V. S. Gerdjikov

  2. Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    V. S. Gerdjikov

  3. Sankt-Petersburg Department of Steklov Mathematical Institute of Russian Academy of Sciences, St-Petersburg, Russia

    V. B. Matveev

  4. Institut de Mathématiques de Bourgogne, UMR 5584-CNRS, Université de Bourgogne - Franche Comté, Dijon Cedex, France

    V. B. Matveev

Authors
  1. A. O. Smirnov
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  2. V. S. Gerdjikov
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  3. V. B. Matveev
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Correspondence to A. O. Smirnov.

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In memory of Boris Dubrovin and Viktor Enol’skii.

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Smirnov, A.O., Gerdjikov, V.S. & Matveev, V.B. From generalized Fourier transforms to spectral curves for the Manakov hierarchy. II. Spectral curves for the Manakov hierarchy. Eur. Phys. J. Plus 135, 561 (2020). https://doi.org/10.1140/epjp/s13360-020-00588-1

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