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The European Physical Journal Special Topics

, Volume 223, Issue 1, pp 43–62 | Cite as

Rogue waves and solitons on a cnoidal background

  • D.J. Kedziora
  • A. Ankiewicz
  • N. Akhmediev
Review
Part of the following topical collections:
  1. Localized Structures in Physics and Chemistry

Abstract

Solutions of the nonlinear Schrödinger equation, appearing as rogue waves on a spatially-periodic background envelope, are obtained using the Darboux transformation scheme. Several particular examples are illustrated numerically. These include soliton and breather solutions on a periodic background as well as higher-order structures. The results enrich our knowledge of possible analytic solutions that describe the appearance of rogue waves in a variety of situations. This work is prepared on the occasion of Prof. Helmut Brand's 60th birthday. He has made significant contributions to the science of solitons and his ideas have inspired our research into localised formations in various physical contexts.

Keywords

Soliton European Physical Journal Special Topic Rogue Wave Darboux Transformation Jacobi Elliptic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2014

Authors and Affiliations

  • D.J. Kedziora
    • 1
  • A. Ankiewicz
    • 1
  • N. Akhmediev
    • 1
  1. 1.Optical Sciences Group, Research School of Physics and Engineering, The Australian National UniversityCanberra ACTAustralia

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