Theoretical and Mathematical Physics

, Volume 186, Issue 2, pp 156–182 | Cite as

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

  • V. B. MatveevEmail author
  • A. O. Smirnov


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.


rogue wave freak wave nonlinear Schrödinger equation Hirota equation AKNS hierarchy 


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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.St. Petersburg State University for Aerospace Instrumentation (SUAI)St. PetersburgRussia
  2. 2.Institut de Mathématiques de BourgogneUniversité de Bourgogne-Franche ComtéDijonFrance

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