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Abstract

Rogue wave (RW) is one of the most fascinating phenomena in nature and has been observed recently in nonlinear optics and water wave tanks. It is considered as a large and spontaneous nonlinear wave and seems to appear from nowhere and disappear without a trace. The Fokas system is the simplest two-dimensional nonlinear evolution model. In this paper, we firstly study a similarity transformation for transforming the system into a long wave-short wave resonance model. Secondly, based on the similarity transformation and the known rational form solution of the long-wave-short-wave resonance model, we give the explicit expressions of the rational function form solutions by means of an undetermined function of the spatial variable y, which is selected as the Hermite function. Finally, we investigate the rich two-dimensional rogue wave excitation and discuss the control of its amplitude and shape, and reveal the propagation characteristics of two-dimensional rogue wave through graphical representation under choosing appropriate free parameter. The results show that the two-dimensional rogue wave structure is controlled by four parameters: ${\rho _0},\;n,\;k,\;{\rm{and}}\;\omega \left( {{\rm{or}}\;\alpha } \right)$ . The parameter $ {\rho _0}$ controls directly the amplitude of the two-dimensional rogue wave, and the larger the value of $ {\rho _0}$ , the greater the amplitude of the amplitude of the two-dimensional rogue wave is. The peak number of the two-dimensional rogue wave in the $(x,\;y)$ and $(y,\;t)$ plane depends on merely the parameter nbut not on the parameter k. When $n = 0,\;1,\;2, \cdots$ , only single peak appears in the $(x,\;t)$ plane, but single peak, two peaks to three peaks appear in the $(x,\;y)$ and $(y,\;t)$ plane, respectively, for the two-dimensional rogue wave of Fokas system. We can find that the two-dimensional rogue wave occurs from the zero background in the $(x,\;t)$ plane, but the two-dimensional rogue wave appears from the line solitons in the $(x,\;y)$ plane and $(y,\;t)$ plane. It is worth pointing out that the rogue wave obtained here can be used to describe the possible physical mechanism of rogue wave phenomenon, and may have potential applications in other (2 + 1)-dimensional nonlinear local or nonlocal models.

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Authors and contacts

Corresponding author:Zhang Jie-Fang,Zhangjief@cuz.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 61877053)

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References

[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
[55]

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[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
[17]
[18]
[19]
[20]
[21]
[22]
[23]
[24]
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
[40]
[41]
[42]
[43]
[44]
[45]
[46]
[47]
[48]
[49]
[50]
[51]
[52]
[53]
[54]
[55]

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[2]	Zhang Jie-Fang, Yu Ding-Guo, Jin Mei-Zhen.Self-similar transformation and excitation of rogue waves for (2+1)-dimensional Zakharov equation. Acta Physica Sinica, 2022, 71(8): 084204.doi:10.7498/aps.71.20211181
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[5]	Chen Hai-Jun, Li Xiang-Fu.The stability of matter-wave solitons in 2D linear and nonlinear optical lattices. Acta Physica Sinica, 2013, 62(7): 070302.doi:10.7498/aps.62.070302
[6]	Lu Da-Quan, Hu Wei.Two-dimensional asynchronous fractional Fourier transform and propagation properties of beams in strongly nonlocal nonlinear medium with an elliptically symmetric response. Acta Physica Sinica, 2013, 62(8): 084211.doi:10.7498/aps.62.084211
[7]	Hu Wen-Cheng, Zhang Jie-Fang, Zhao Bi, Lou Ji-Hui.Transmission control of nonautonomous optical rogue waves in nonlinear optical media. Acta Physica Sinica, 2013, 62(2): 024216.doi:10.7498/aps.62.024216
[8]	Ma Zheng-Yi, Ma Song-Hua, Yang Yi.Rational solutions and spatial solitons for the (2+1)-dimensional nonlinear Schrdinger equation with distributed coefficients. Acta Physica Sinica, 2012, 61(19): 190508.doi:10.7498/aps.61.190508
[9]	Qian Cun, Wang Liang-Liang, Zhang Jie-Fang.Solitons of nonlinear Schrödinger equation withvariable-coefficients and interaction. Acta Physica Sinica, 2011, 60(6): 064214.doi:10.7498/aps.60.064214
[10]	Zhang Bo, Xie Fan, Yang Ru.Study on border collision and bifurcation of two-dimensional piecewise smooth systems in current mode controlled Buck converter. Acta Physica Sinica, 2010, 59(12): 8393-8406.doi:10.7498/aps.59.8393
[11]	Zhang Li-Sheng, Deng Min-Yi, Kong Ling-Jiang, Liu Mu-Ren, Tang Guo-Ning.The cellular automaton model for the nonlinear waves in the two-dimensional excitable media. Acta Physica Sinica, 2009, 58(7): 4493-4499.doi:10.7498/aps.58.4493
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[13]	Zheng Chun-Long, Zhang Jie-Fang.. Acta Physica Sinica, 2002, 51(11): 2426-2430.doi:10.7498/aps.51.2426
[14]	Zhang Jie-Fang, Huang Wen-Hua, Zheng Chun-Long.Coherent soliton structures of a new (2+1) dimensional evolution equation. Acta Physica Sinica, 2002, 51(12): 2676-2682.doi:10.7498/aps.51.2676
[15]	Dong Quan-Lin, Liu Bin.. Acta Physica Sinica, 2002, 51(10): 2191-2196.doi:10.7498/aps.51.2191
[16]	CHEN YAN-SONG, ZHENG SHI-HAI, LI DE-HUA.TWO-DIMENSIONAL OPTICAL GEOMETRIC MOMENT TRANSFORM. Acta Physica Sinica, 1991, 40(10): 1601-1606.doi:10.7498/aps.40.1601
[17]	ZHENG SHI-HAI, CHEN YAN-SONG, LI DE-HUA.REALIZATION OF TWO-DIMENSIONAL MELLIN TRANSFORM. Acta Physica Sinica, 1990, 39(5): 749-753.doi:10.7498/aps.39.749
[18]	WANG LI, DONG BI-ZHEN, YANG GUO-ZHEN.THE TWO-DIMENSIONAL PHASE RETRIEVAL PROBLEM IN NON-UNITARY TRANSFORM SYSTEM. Acta Physica Sinica, 1989, 38(11): 1809-1817.doi:10.7498/aps.38.1809
[19]	DU YI-JING, CHEN LI-RONG, YAN ZU-TONG.A STATISTICAL THEORY OF THE COLLINS' MODEL IN THE PHASE TRANSITION OF TWO-DIMENSIONAL SYSTEM. Acta Physica Sinica, 1983, 32(1): 96-102.doi:10.7498/aps.32.96
[20]	HUANG YONG-REN.TWO DIMENSIONAL DYNAMICAL NMR SPECTRUM IN WEAK COUPLED TWO SPIN (I=l/2) SYSTEM. Acta Physica Sinica, 1982, 31(9): 1141-1151.doi:10.7498/aps.31.1141

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Vol. 69, Issue 21 - 2020-11-05

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