Rogue wave-type solutions of the mKdV equation and their relation to known NLSE rogue wave solutions

A. Ankiewicz; N. Akhmediev

doi:10.1007/s11071-017-3991-2

Rogue wave-type solutions of the mKdV equation and their relation to known NLSE rogue wave solutions

A. Ankiewicz^*, N. Akhmediev

^*Corresponding author for this work

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

59 Citations (Scopus)

Abstract

We present the first four exact rational solutions of the set of rational solutions of the modified Korteweg–de Vries equation. These solutions can be considered as rogue waves of the corresponding equation. Comparison with rogue wave solutions of the nonlinear Schrödinger equation shows a strong analogy between their characteristics, especially for amplitude-to-background ratio. The new solutions may be useful in the theory of rogue waves in shallow water and for light propagation in cubic nonlinear media involving only a few optical cycles.

Original language	English
Pages (from-to)	1931-1938
Number of pages	8
Journal	Nonlinear Dynamics
Volume	91
Issue number	3
DOIs	https://doi.org/10.1007/s11071-017-3991-2
Publication status	Published - 1 Feb 2018

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title = "Rogue wave-type solutions of the mKdV equation and their relation to known NLSE rogue wave solutions",

abstract = "We present the first four exact rational solutions of the set of rational solutions of the modified Korteweg–de Vries equation. These solutions can be considered as rogue waves of the corresponding equation. Comparison with rogue wave solutions of the nonlinear Schr{\"o}dinger equation shows a strong analogy between their characteristics, especially for amplitude-to-background ratio. The new solutions may be useful in the theory of rogue waves in shallow water and for light propagation in cubic nonlinear media involving only a few optical cycles.",

keywords = "Modified Korteweg–de Vries, Rational solutions, Rogue waves, Shallow water",

author = "A. Ankiewicz and N. Akhmediev",

note = "Publisher Copyright: {\textcopyright} 2017, Springer Science+Business Media B.V., part of Springer Nature.",

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N2 - We present the first four exact rational solutions of the set of rational solutions of the modified Korteweg–de Vries equation. These solutions can be considered as rogue waves of the corresponding equation. Comparison with rogue wave solutions of the nonlinear Schrödinger equation shows a strong analogy between their characteristics, especially for amplitude-to-background ratio. The new solutions may be useful in the theory of rogue waves in shallow water and for light propagation in cubic nonlinear media involving only a few optical cycles.

AB - We present the first four exact rational solutions of the set of rational solutions of the modified Korteweg–de Vries equation. These solutions can be considered as rogue waves of the corresponding equation. Comparison with rogue wave solutions of the nonlinear Schrödinger equation shows a strong analogy between their characteristics, especially for amplitude-to-background ratio. The new solutions may be useful in the theory of rogue waves in shallow water and for light propagation in cubic nonlinear media involving only a few optical cycles.

KW - Modified Korteweg–de Vries

KW - Rational solutions

KW - Rogue waves

KW - Shallow water

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DO - 10.1007/s11071-017-3991-2

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JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

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ER -

Rogue wave-type solutions of the mKdV equation and their relation to known NLSE rogue wave solutions

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