Nonlinear Talbot effect of rogue waves

Yiqi Zhang; Milivoj R. Belić; Huaibin Zheng; Haixia Chen; Changbiao Li; Jianping Song; Yanpeng Zhang

doi:10.1103/PhysRevE.89.032902

Nonlinear Talbot effect of rogue waves

Yiqi Zhang^*
, Milivoj R. Belić
, Huaibin Zheng
, Haixia Chen
, Changbiao Li
, Jianping Song
, Yanpeng Zhang^*

^*Corresponding author for this work

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

61 Citations (Scopus)

Abstract

Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.

Original language	English
Article number	032902
Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume	89
Issue number	3
DOIs	https://doi.org/10.1103/PhysRevE.89.032902
Publication status	Published - 5 Mar 2014
Externally published	Yes

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title = "Nonlinear Talbot effect of rogue waves",

abstract = "Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schr{\"o}dinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.",

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doi = "10.1103/PhysRevE.89.032902",

language = "English",

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T1 - Nonlinear Talbot effect of rogue waves

AU - Zhang, Yiqi

AU - Belić, Milivoj R.

AU - Zheng, Huaibin

AU - Chen, Haixia

AU - Li, Changbiao

AU - Song, Jianping

AU - Zhang, Yanpeng

PY - 2014/3/5

Y1 - 2014/3/5

N2 - Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.

AB - Akhmediev and Kuznetsov-Ma breathers are rogue wave solutions of the nonlinear Schrödinger equation (NLSE). Talbot effect (TE) is an image recurrence phenomenon in the diffraction of light waves. We report the nonlinear TE of rogue waves in a cubic medium. It is different from the linear TE, in that the wave propagates in a NL medium and is an eigenmode of NLSE. Periodic rogue waves impinging on a NL medium exhibit recurrent behavior, but only at the TE length and at the half-TE length with a π-phase shift; the fractional TE is absent. The NL TE is the result of the NL interference of the lobes of rogue wave breathers. This interaction is related to the transverse period and intensity of breathers, in that the bigger the period and the higher the intensity, the shorter the TE length.

UR - https://www.scopus.com/pages/publications/84899000403

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DO - 10.1103/PhysRevE.89.032902

M3 - Article

AN - SCOPUS:84899000403

SN - 1539-3755

VL - 89

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 3

M1 - 032902

ER -

Nonlinear Talbot effect of rogue waves

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