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Resonance rogue wave prediction

  • School of Physical Science and Technology, Ningbo University, Ningbo 315211, China

Cite this:
https://doi.org/10.3969/j.issn.0253-2778.2020.02.006
  • Received Date: 07 July 2018
  • Accepted Date: 02 August 2018
  • Rev Recd Date: 02 August 2018
  • Publish Date: 28 February 2020
    Abstract

  • Abstract

    Rogue wave is a kind of local wave with very steep distribution, very short existence time, and whose peak value is much higher than the surrounding waves. Therefore, taking the (2+1)-dimensional SK equation as an example, the Hirota bilinear method was used to explore a new type of rogue wave(resonance rogue wave), whose formation is closely related to the lump-type soliton. When the lump-type soliton is under the influence of a double-striped soliton, it will appear only momentarily and then disappear immediately, so it becomes a rogue wave. And the characteristic quantities such as the movement track, the existence time, the area and the volume of the strange wave were obtained by the method of theoretical calculation and the combination of number and shape.

    Abstract

    Rogue wave is a kind of local wave with very steep distribution, very short existence time, and whose peak value is much higher than the surrounding waves. Therefore, taking the (2+1)-dimensional SK equation as an example, the Hirota bilinear method was used to explore a new type of rogue wave(resonance rogue wave), whose formation is closely related to the lump-type soliton. When the lump-type soliton is under the influence of a double-striped soliton, it will appear only momentarily and then disappear immediately, so it becomes a rogue wave. And the characteristic quantities such as the movement track, the existence time, the area and the volume of the strange wave were obtained by the method of theoretical calculation and the combination of number and shape.
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    • References(29)
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    YAN Z . Vector financial rogue waves[J]. Physics Letters A, 2011, 375(48): 4274-4279.
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    ZHANG X,CHEN Y. Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation[J].Communications in Nonlinear Science and Numerical Simulation, 2017, 52: 24-31.
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    HUANG L L, CHEN Y. Lump solutions and interaction phenomenon for (2+1)-dimensional Sawada-Kotera equation[J]. Communications in Theoretical Physics, 2017, 67(5): 473-478.
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    ZHENG P F, JIA M. A more general form of lump solution, lumpoff, and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation[J]. Chin Phys B, 2018, 27(12): 120201.
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    [22]
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    [23]
    JIA S L, GAO Y T, HU W Q, et al. Solitons and breather waves for a (2+1)-dimensional Sawada-Kotera equation[J]. Modern Physics Letters B, 2017, 31(22): 1750129.
    [24]
    FERMI E, PASTA J, ULAM S. Studies of nonlinear problems[R]. Los Alamos, NM: Los Alamos Scientific Lab, 1955: Report No. LA-1940.
    [25]
    LANDOU L D, LIFSHITZ E M. Mechanics[M]. 3rd ed. Moscow: Nauka, 1993: 79.
    [26]
    ZHANG X, CHEN Y. Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation[J]. Communications in Nonlinear Science Numerical Simulation, 2017, 52: 24-31.
    [27]
    CHEN M D, LI X, WANG Y, et al. A pair of resonance stripe solitons and lump solutions to a reduced (3+1)-dimensional nonlinear evolution equation[J]. Communications in Theoretical Physics, 2017, 67(6): 595-600.
    [28]
    HUANG L L, CHEN Y. Lump solutions and interaction phenomenon for (2+1)-dimensional Sawada-Kotera equation[J]. Communications in Theoretical Physics, 2017, 67(5): 473-478.
    [29]
    ZHANG Xiaoen, CHEN Yong. Deformation rogue wave to the (2+1)-dimensional KdV equation[J]. Nonliear Dynamics, 2017, 90: 755-763.)
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    [1]
    LAVRENOV I V. The wave energy concentration at the Agulhas current off South Africa[J]. Natural Hazards, 1998, 17(2):117-127.
    [2]
    LAWTON G. Monsters of the deep (the perfect wave)[J]. New Scientist, 2001, 170(2297): 28-32.
    [3]
    KJELDSEN S P. Dangerous wave groups[J]. Norwegian Maritime Research, 1984, 12(2): 4-6.
    [4]
    DIEKISON D. Huge waves[J]. Outside Magazine, 1995: 3-5.
    [5]
    HAVER S. A possible freak wave event measured at the Draupner Jacket January 1 1995[C]// Rogue Waves 2004. Brest, France: Ifremer, 2004：1-8.
    [6]
    WARWIEK R W. Hurricane Luis, the Queen Elizabeth 2 and a rogue wave[J]. Marine Observer, 1996, 66: 134.
    [7]
    HOLLIDAY N P, YELLAND M J, PASEAL R W, et al. Were extreme waves in the Rockall through the largest ever recorded? [J]. Geophysical Research Letters, 2006, 33(5): 151-162.
    [8]
    DIDENKULOVA I I, SLUNYAEV A V, PELINOVSKY E N, et al. Freak waves in 2005[J]. Natural Hazards and Earth System Sciences,2006, 6: 1007-1015.
    [9]
    SOLLI D R, ROPERS C, KOONATH P, et al. Optical rogue waves[J]. Nature,2007, 54: 1054-1057.
    [10]
    KIBLER B, FATOME J, FINOT C, et al. The Peregrine soliton in nonlinear fibre optics[J]. Nature Physics, 2010, 6(10): 790-795.
    [11]
    LAVEDER D, PASSOT T T, SULEM P, et al. Rogue waves in Alfvénic turbulence[J]. Physics Letters A, 2011, 375: 3997-4002.
    [12]
    BLUDOV Y, KONOTOP V, AKHMEDIEV N. Matter rogue waves[J]. Physical Review A, 2009, 80(3): 033610.
    [13]
    MOSLEM W M, SHUKLA P K,ELIASSON B. Surface plasma rogue waves[J]. Europhys Lett, 2011, 96(2): 25002- 25005.
    [14]
    MOSLEM W M, SABRY R, EL-LABANY S K, et al. Dust-acoustic rogue waves in a nonextensive plasma[J]. Physical Review E, 2011, 84(6): 066402.
    [15]
    YAN Z, KONOTOP V V, AKHMEDIEV N. Three-dimensional rogue waves in nonstationary parabolic potentials[J]. Phys Rev E, 2010, 82: 036610.
    [16]
    YAN Zhenya. Financial rogue waves[J]. Communications in Theoretical Physics, 2010, 54： 947-949.
    [17]
    YAN Z . Vector financial rogue waves[J]. Physics Letters A, 2011, 375(48): 4274-4279.
    [18]
    ZHANG X,CHEN Y. Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation[J].Communications in Nonlinear Science and Numerical Simulation, 2017, 52: 24-31.
    [19]
    HUANG L L, CHEN Y. Lump solutions and interaction phenomenon for (2+1)-dimensional Sawada-Kotera equation[J]. Communications in Theoretical Physics, 2017, 67(5): 473-478.
    [20]
    ZHENG P F, JIA M. A more general form of lump solution, lumpoff, and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation[J]. Chin Phys B, 2018, 27(12): 120201.
    [21]
    ZOU L, YU Z B, TIAN S F, et al. Lump solutions with interaction phenomena in the (2+1)-dimensional Ito equation[J]. Modern Physics Letters B, 2018: 1850104.
    [22]
    ZHANG Xiaoen, CHEN Yong. Rogue wave and a pair of resonance stripe solitons to a reduced generalized (3+1)-dimensional KP equation[DB/OL]. [2018-01-01]. https://arxiv.org/abs/1610.09507.
    [23]
    JIA S L, GAO Y T, HU W Q, et al. Solitons and breather waves for a (2+1)-dimensional Sawada-Kotera equation[J]. Modern Physics Letters B, 2017, 31(22): 1750129.
    [24]
    FERMI E, PASTA J, ULAM S. Studies of nonlinear problems[R]. Los Alamos, NM: Los Alamos Scientific Lab, 1955: Report No. LA-1940.
    [25]
    LANDOU L D, LIFSHITZ E M. Mechanics[M]. 3rd ed. Moscow: Nauka, 1993: 79.
    [26]
    ZHANG X, CHEN Y. Rogue wave and a pair of resonance stripe solitons to a reduced (3+1)-dimensional Jimbo-Miwa equation[J]. Communications in Nonlinear Science Numerical Simulation, 2017, 52: 24-31.
    [27]
    CHEN M D, LI X, WANG Y, et al. A pair of resonance stripe solitons and lump solutions to a reduced (3+1)-dimensional nonlinear evolution equation[J]. Communications in Theoretical Physics, 2017, 67(6): 595-600.
    [28]
    HUANG L L, CHEN Y. Lump solutions and interaction phenomenon for (2+1)-dimensional Sawada-Kotera equation[J]. Communications in Theoretical Physics, 2017, 67(5): 473-478.
    [29]
    ZHANG Xiaoen, CHEN Yong. Deformation rogue wave to the (2+1)-dimensional KdV equation[J]. Nonliear Dynamics, 2017, 90: 755-763.)
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