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Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach

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Abstract

We describe a unified structure of solutions for all equations of the Ablowitz–Kaup–Newell–Segur hierarchy and their combinations. We give examples of solutions that satisfy different equations for different parameter values. In particular, we consider a rank-2 quasirational solution that can be used to investigate many integrable models in nonlinear optics. An advantage of our approach is the possibility to investigate changes in the behavior of a solution resulting from changing the model.

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Authors and Affiliations

  1. St. Petersburg State University for Aerospace Instrumentation (SUAI), St. Petersburg, Russia

    V. B. Matveev & A. O. Smirnov

  2. Institut de Mathématiques de Bourgogne, Université de Bourgogne-Franche Comté, Dijon, France

    V. B. Matveev

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

Additional information

This research is supported by the Russian Foundation for Basic Research (Grant No. 14-01-00589 a).

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 186, No. 2, pp. 191–220, February, 2016. Original article submitted April 28, 2015; revised August 31, 2015.

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Matveev, V.B., Smirnov, A.O. Solutions of the Ablowitz–Kaup–Newell–Segur hierarchy equations of the “rogue wave” type: A unified approach. Theor Math Phys 186, 156–182 (2016). https://doi.org/10.1134/S0040577916020033

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