Rogue waves and rational solutions of the Hirota equation

Adrian Ankiewicz; J. M. Soto-Crespo; Nail Akhmediev

doi:10.1103/PhysRevE.81.046602

Rogue waves and rational solutions of the Hirota equation

Adrian Ankiewicz^*, J. M. Soto-Crespo, Nail Akhmediev

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

451 Citations (Scopus)

Abstract

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.

Original language	English
Article number	046602
Journal	Physical Review E
Volume	81
Issue number	4
DOIs	https://doi.org/10.1103/PhysRevE.81.046602
Publication status	Published - 15 Apr 2010

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10.1103/PhysRevE.81.046602

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AB - 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.

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Rogue waves and rational solutions of the Hirota equation

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