Systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds

Stanko N. Nikolić; Najdan B. Aleksić; Omar A. Ashour; Milivoj R. Belić; Siu A. Chin

doi:10.1007/s11071-017-3540-z

Systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds

Stanko N. Nikolić^*, Najdan B. Aleksić, Omar A. Ashour, Milivoj R. Belić, Siu A. Chin

^*Corresponding author for this work

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

15 Citations (Scopus)

Abstract

We investigate the systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds. The Darboux transformation is used to construct proper initial conditions for dynamical generation of high-intensity solitons and breathers of different orders on a uniform background. We provide expressions for the Lax pair generating functions and the procedure for calculating higher-order solutions when Jacobi elliptic functions are the background seed solutions of the Hirota equation. We confirm that the peak height of each soliton or breather in the nonlinear Darboux superposition adds linearly, to form the intensity maximum of the final solution.

Original language	English
Pages (from-to)	1637-1649
Number of pages	13
Journal	Nonlinear Dynamics
Volume	89
Issue number	3
DOIs	https://doi.org/10.1007/s11071-017-3540-z
Publication status	Published - 1 Aug 2017
Externally published	Yes

Keywords

Breathers and rogue waves
Darboux transformation
Higher-order solitons
Hirota equation

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10.1007/s11071-017-3540-z

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abstract = "We investigate the systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds. The Darboux transformation is used to construct proper initial conditions for dynamical generation of high-intensity solitons and breathers of different orders on a uniform background. We provide expressions for the Lax pair generating functions and the procedure for calculating higher-order solutions when Jacobi elliptic functions are the background seed solutions of the Hirota equation. We confirm that the peak height of each soliton or breather in the nonlinear Darboux superposition adds linearly, to form the intensity maximum of the final solution.",

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AU - Nikolić, Stanko N.

AU - Aleksić, Najdan B.

AU - Ashour, Omar A.

AU - Belić, Milivoj R.

AU - Chin, Siu A.

PY - 2017/8/1

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N2 - We investigate the systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds. The Darboux transformation is used to construct proper initial conditions for dynamical generation of high-intensity solitons and breathers of different orders on a uniform background. We provide expressions for the Lax pair generating functions and the procedure for calculating higher-order solutions when Jacobi elliptic functions are the background seed solutions of the Hirota equation. We confirm that the peak height of each soliton or breather in the nonlinear Darboux superposition adds linearly, to form the intensity maximum of the final solution.

AB - We investigate the systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds. The Darboux transformation is used to construct proper initial conditions for dynamical generation of high-intensity solitons and breathers of different orders on a uniform background. We provide expressions for the Lax pair generating functions and the procedure for calculating higher-order solutions when Jacobi elliptic functions are the background seed solutions of the Hirota equation. We confirm that the peak height of each soliton or breather in the nonlinear Darboux superposition adds linearly, to form the intensity maximum of the final solution.

KW - Breathers and rogue waves

KW - Darboux transformation

KW - Higher-order solitons

KW - Hirota equation

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JF - Nonlinear Dynamics

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Systematic generation of higher-order solitons and breathers of the Hirota equation on different backgrounds

Abstract

Keywords

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