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Rogue waves and rational solutions of the Hirota equation Adrian Ankiewicz,1
 

Summary: Rogue waves and rational solutions of the Hirota equation
Adrian Ankiewicz,1
J. M. Soto-Crespo,2
and Nail Akhmediev1
1
Optical Sciences Group, Research School of Physics and Engineering, Institute of Advanced Studies,
The Australian National University, Canberra, Australian Capital Territory 0200, Australia
2
Instituto de Óptica, CSIC, Serrano 121, 28006 Madrid, Spain
Received 12 November 2009; published 15 April 2010
The Hirota equation is a modified nonlinear Schrödinger equation NLSE that takes into account higher-
order dispersion and time-delay corrections to the cubic nonlinearity. In describing wave propagation in the
ocean and optical fibers, it can be viewed as an approximation which is more accurate than the NLSE. We have
modified the Darboux transformation technique to show how to construct the hierarchy of rational solutions of
the Hirota equation. We present explicit forms for the two lower-order solutions. Each one is a regular
nonsingular rational solution with a single maximum that can describe a rogue wave in this model. Numerical
simulations reveal the appearance of these solutions in a chaotic field generated from a perturbed continuous
wave solution.
DOI: 10.1103/PhysRevE.81.046602 PACS number s : 42.65.Tg, 47.20.Ky, 47.35.Fg
I. INTRODUCTION

  

Source: Akhmediev, Nail - Research School of Physical Sciences and Engineering, Australian National University
Australian National University, Research School of Physical Sciences and Engineering, Optical Sciences Group

 

Collections: Engineering; Physics