Discrete rogue waves of the Ablowitz-Ladik and Hirota equations

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

doi:10.1103/PhysRevE.82.026602

Discrete rogue waves of the Ablowitz-Ladik and Hirota equations

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

^*Corresponding author for this work

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

171 Citations (Scopus)

Abstract

We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which includes, as particular cases, both the discrete Ablowitz-Ladik equation and the discrete modified Korteweg-de Vries (mKdV) equation.

Original language	English
Article number	026602
Journal	Physical Review E
Volume	82
Issue number	2
DOIs	https://doi.org/10.1103/PhysRevE.82.026602
Publication status	Published - 11 Aug 2010

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10.1103/PhysRevE.82.026602

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title = "Discrete rogue waves of the Ablowitz-Ladik and Hirota equations",

abstract = "We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schr{\"o}dinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which includes, as particular cases, both the discrete Ablowitz-Ladik equation and the discrete modified Korteweg-de Vries (mKdV) equation.",

author = "Adrian Ankiewicz and Nail Akhmediev and Soto-Crespo, \{J. M.\}",

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AU - Soto-Crespo, J. M.

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N2 - We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which includes, as particular cases, both the discrete Ablowitz-Ladik equation and the discrete modified Korteweg-de Vries (mKdV) equation.

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Discrete rogue waves of the Ablowitz-Ladik and Hirota equations

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