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KESİKLİ KDV DENKLEMİNDE ROGUE DALGALARI

Yıl 2024, Cilt: 12 Sayı: 1, 55 - 61, 27.02.2024
https://doi.org/10.20290/estubtdb.1357676

Öz

Bu çalışma, kesikli KdV denklemiyle tanımlanan bir dizi dalga kılavuzunu ele almaktadır. Periyodik ve kaybolmayan sınır koşulları altında dKdV denklemi için rogue dalga çözümleri nümerik olarak türetilmiştir. dKdV denklemi periyodik sınır koşullarında çözüldüğünde, şok ön kırılmasından dolayı kesikli rogue dalgası meydana gelir. Ayrıca dKdV denklemi kaybolmayan sınır koşulları altında nümerik olarak çözülmüştür ve rogue dalga genliğinin ρ_0 parametresine bağlı olduğu bulunmuştur.

Destekleyen Kurum

This study is supported by Kırklareli University Scientific Research Projects Coordination Unit under grant no: KLÜUBAP208

Proje Numarası

KLÜUBAP208

Kaynakça

  • [1] Kharif C, Pelinovsky E and Slunyaev A. Rogue waves in the ocean. Springer, 2008.
  • [2] Guo B, Tian L, Yan Z, Ling L and Wang YF. Rogue Waves: Mathematical Theory and Applications in Physics. Walter de Gruyter, 2017.
  • [3] White BS and Fornberg B. On the chance of freak waves at sea. J. Fluid Mech. 1998; 355, 113-138.
  • [4] Andrade MA. Physical mechanisms of the rogue wave phenomenon. The University of Arizona, 2017.
  • [5] Onorato M, Residori S and Baronio F. Rogue and shock waves in nonlinear dispersive media. Springer, 926, 2016.
  • [6] Haver S. A possible freak wave event measured at the Draupner Jacket January 1 1995. 1-8, 2004.
  • [7] Dudley JM, Genty G, Dias F, Kibler B and Akhmediev N. Modulation instability, akhmediev breathers and continuous wave supercontinuum generation. Opt. Express 2009; 17, 21497-21508.
  • [8] Dudley JM, Genty G and Eggleton BJ. Harnessing and control of optical rogue waves in supercontinuum generation. Opt. Express 2008; 163644-3651.
  • [9] Erkintalo M, Hammani K, Kibler B and Finot C. Higher-order modulation instability in nonlinear fiber optics. Phys. Rev. Lett. 2011; 107, 253901.
  • [10] Akhmediev NN and Korneev V I. Modulation instability and periodic solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 1986; 69, 1089-1093.
  • [11] Tulin MP and Waseda T. Laboratory observations of wave group evolution, including breaking effects. J. Fluid Mech. 1999; 378, 197-232.
  • [12] Kharif C and Pelinovsky E. Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B/Fluids. 2003; 22, 603-634.
  • [13] Peregrine DH. Water waves, nonlinear Schrödinger equations and their solutions. J. Aust. Math. Soc. Ser. B. Appl. Math 1983; 25, 16-43.
  • [14] Shrira V I and Geojaev VV. What makes the Peregrine soliton so special as a prototype of freak waves?. J. Eng. Math. 2010; 67, 11-22.
  • [15] Chen J and Pelinovsky DE. Rogue periodic waves of the modified KdV equation. Nonlinearity 2018; 31, 1955-1980.
  • [16] Chen J and Pelinovsky DE. Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background. J. Nonlinear Sci. 2019; 29, 2797-2843.
  • [17] Slunyaev AV and Pelinovsky EN. Role of multiple soliton interactions in the generation of rogue waves: the modified Korteweg de Vries framework. Phys. Rev. Lett. 2016; 117, 214501.
  • [18] Grimshaw R, Pelinovsky E, Taipova T and Sergeeva A. Rogue internal waves in the ocean: long wave model. Eur Phys J Spec Top. 2010; 185, 195-208.
  • [19] Ankiewicz A, Akhmediev N and Soto-Crespo JM. Discrete rogue waves of the ablowitz-ladik and hirota equations. Phys. Rev. E. 2010; 82, 026602.
  • [20] He J, Xu S and Porsezian K. Rogue waves of the fokas-lenells equation. J. Phys. Soc. Japan. 2012; 81, 124007.
  • [21] Ohta Y and Yang J. Dynamics of rogue waves in the Davey Stewartson II equation. J. Phys. A Math. Theor. 2013; 46, 105202.
  • [22] Russell JS. The Wave of Translation in the Oceans of Water. Air and Ether, London, 1895.
  • [23] Rayleigh L. On waves. Phil. Mag. 1876; 1, 257-259.
  • [24] Boussinesq JV. Theorie generale des mouvements qui sont propages dans un canal rectangulaire horizontal. CR Acad. Sci.1871; Paris, 73.
  • [25] Korteweg DJ and De Vries G. XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Lond. Edinb. Dublin philos. mag. j. sci. 1895; 39, 422-443.
  • [26] Zabusky NJ and Kruskal MD. Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 1965; 15, 240.
  • [27] Pelinovsky E, Talipova T and Kharif C. Nonlinear-dispersive mechanism of the freak wave formation in shallow water. Phys. D: Nonlinear Phenom. 2000; 147, 83-94.
  • [28] Bludov YV, Konotop VV and Akhmediev N. Rogue waves as spatial energy concentrators in arrays of nonlinear waveguides. Opt. Lett. 2009; 34, 3015-3017.
  • [29] Narita K. Soliton solutions for the coupled discrete KdV equations under non-vanishing boundary conditions at infinity. J. Phys. Soc. Japan. 2002; 71, 2401-2405.
  • [30] Efe S and Yuce C. Discrete rogue waves in an array of waveguides. Phys. Lett. A 2015; 379,1251 1255.
  • [31] Solli DR, Ropers C, Koonath P and Jalali B. Optical rogue waves. Nat. Phys. 2007; 450, 1054 1057.
  • [32] Kibler B, Fatome J, Finot C, Millot G, Dias F, Genty G, Akhmediev N and Dudley JM. The peregrine soliton in nonlinear fibre optics. Nat. Phys. 2010; 6, 790-795.
  • [33] Moslem WM. Langmuir rogue waves in electron-positron plasmas. Phys. Plasmas. 2011; 18, 032301.
  • [34] Hirota R. Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation. J. Phys. Soc. Jpn 1977; 43, 1424-1433.
  • [35] Ankiewicz A, Bokaeeyan M and Akhmediev N. Shallow-water rogue waves: An approach based on complex solutions of the Korteweg de Vries equation. Phys. Rev. E. 2019; 99, 050201.
  • [36] Crabb M and Akhmediev N. “Rogue wave multiplets in the complex KdV equation",arXiv preprint arXiv:2009.09831, 2020.

ROGUE WAVES IN DISCRETE KDV EQUATION

Yıl 2024, Cilt: 12 Sayı: 1, 55 - 61, 27.02.2024
https://doi.org/10.20290/estubtdb.1357676

Öz

This study considers an array of waveguides described by a discrete KdV equation. Rogue wave solutions numerically derive for the dKdV equation under periodic and non-vanishing boundary conditions. When solving the dKdV equation with periodic boundary conditions, a discrete rogue wave occurs due to shock front breaking. Additionally, the dKdV equation has been solved numerically under non-vanishing boundary conditions, and it has been found that the rogue wave amplitude depends on the ρ_0 parameter.

Proje Numarası

KLÜUBAP208

Kaynakça

  • [1] Kharif C, Pelinovsky E and Slunyaev A. Rogue waves in the ocean. Springer, 2008.
  • [2] Guo B, Tian L, Yan Z, Ling L and Wang YF. Rogue Waves: Mathematical Theory and Applications in Physics. Walter de Gruyter, 2017.
  • [3] White BS and Fornberg B. On the chance of freak waves at sea. J. Fluid Mech. 1998; 355, 113-138.
  • [4] Andrade MA. Physical mechanisms of the rogue wave phenomenon. The University of Arizona, 2017.
  • [5] Onorato M, Residori S and Baronio F. Rogue and shock waves in nonlinear dispersive media. Springer, 926, 2016.
  • [6] Haver S. A possible freak wave event measured at the Draupner Jacket January 1 1995. 1-8, 2004.
  • [7] Dudley JM, Genty G, Dias F, Kibler B and Akhmediev N. Modulation instability, akhmediev breathers and continuous wave supercontinuum generation. Opt. Express 2009; 17, 21497-21508.
  • [8] Dudley JM, Genty G and Eggleton BJ. Harnessing and control of optical rogue waves in supercontinuum generation. Opt. Express 2008; 163644-3651.
  • [9] Erkintalo M, Hammani K, Kibler B and Finot C. Higher-order modulation instability in nonlinear fiber optics. Phys. Rev. Lett. 2011; 107, 253901.
  • [10] Akhmediev NN and Korneev V I. Modulation instability and periodic solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 1986; 69, 1089-1093.
  • [11] Tulin MP and Waseda T. Laboratory observations of wave group evolution, including breaking effects. J. Fluid Mech. 1999; 378, 197-232.
  • [12] Kharif C and Pelinovsky E. Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B/Fluids. 2003; 22, 603-634.
  • [13] Peregrine DH. Water waves, nonlinear Schrödinger equations and their solutions. J. Aust. Math. Soc. Ser. B. Appl. Math 1983; 25, 16-43.
  • [14] Shrira V I and Geojaev VV. What makes the Peregrine soliton so special as a prototype of freak waves?. J. Eng. Math. 2010; 67, 11-22.
  • [15] Chen J and Pelinovsky DE. Rogue periodic waves of the modified KdV equation. Nonlinearity 2018; 31, 1955-1980.
  • [16] Chen J and Pelinovsky DE. Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background. J. Nonlinear Sci. 2019; 29, 2797-2843.
  • [17] Slunyaev AV and Pelinovsky EN. Role of multiple soliton interactions in the generation of rogue waves: the modified Korteweg de Vries framework. Phys. Rev. Lett. 2016; 117, 214501.
  • [18] Grimshaw R, Pelinovsky E, Taipova T and Sergeeva A. Rogue internal waves in the ocean: long wave model. Eur Phys J Spec Top. 2010; 185, 195-208.
  • [19] Ankiewicz A, Akhmediev N and Soto-Crespo JM. Discrete rogue waves of the ablowitz-ladik and hirota equations. Phys. Rev. E. 2010; 82, 026602.
  • [20] He J, Xu S and Porsezian K. Rogue waves of the fokas-lenells equation. J. Phys. Soc. Japan. 2012; 81, 124007.
  • [21] Ohta Y and Yang J. Dynamics of rogue waves in the Davey Stewartson II equation. J. Phys. A Math. Theor. 2013; 46, 105202.
  • [22] Russell JS. The Wave of Translation in the Oceans of Water. Air and Ether, London, 1895.
  • [23] Rayleigh L. On waves. Phil. Mag. 1876; 1, 257-259.
  • [24] Boussinesq JV. Theorie generale des mouvements qui sont propages dans un canal rectangulaire horizontal. CR Acad. Sci.1871; Paris, 73.
  • [25] Korteweg DJ and De Vries G. XLI. On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Lond. Edinb. Dublin philos. mag. j. sci. 1895; 39, 422-443.
  • [26] Zabusky NJ and Kruskal MD. Interaction of solitons in a collisionless plasma and the recurrence of initial states. Phys. Rev. Lett. 1965; 15, 240.
  • [27] Pelinovsky E, Talipova T and Kharif C. Nonlinear-dispersive mechanism of the freak wave formation in shallow water. Phys. D: Nonlinear Phenom. 2000; 147, 83-94.
  • [28] Bludov YV, Konotop VV and Akhmediev N. Rogue waves as spatial energy concentrators in arrays of nonlinear waveguides. Opt. Lett. 2009; 34, 3015-3017.
  • [29] Narita K. Soliton solutions for the coupled discrete KdV equations under non-vanishing boundary conditions at infinity. J. Phys. Soc. Japan. 2002; 71, 2401-2405.
  • [30] Efe S and Yuce C. Discrete rogue waves in an array of waveguides. Phys. Lett. A 2015; 379,1251 1255.
  • [31] Solli DR, Ropers C, Koonath P and Jalali B. Optical rogue waves. Nat. Phys. 2007; 450, 1054 1057.
  • [32] Kibler B, Fatome J, Finot C, Millot G, Dias F, Genty G, Akhmediev N and Dudley JM. The peregrine soliton in nonlinear fibre optics. Nat. Phys. 2010; 6, 790-795.
  • [33] Moslem WM. Langmuir rogue waves in electron-positron plasmas. Phys. Plasmas. 2011; 18, 032301.
  • [34] Hirota R. Nonlinear Partial Difference Equations. I. A Difference Analogue of the Korteweg-de Vries Equation. J. Phys. Soc. Jpn 1977; 43, 1424-1433.
  • [35] Ankiewicz A, Bokaeeyan M and Akhmediev N. Shallow-water rogue waves: An approach based on complex solutions of the Korteweg de Vries equation. Phys. Rev. E. 2019; 99, 050201.
  • [36] Crabb M and Akhmediev N. “Rogue wave multiplets in the complex KdV equation",arXiv preprint arXiv:2009.09831, 2020.
Toplam 36 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Genel Fizik
Bölüm Makaleler
Yazarlar

Semiha Tombuloğlu 0000-0003-2273-5633

Proje Numarası KLÜUBAP208
Yayımlanma Tarihi 27 Şubat 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 12 Sayı: 1

Kaynak Göster

APA Tombuloğlu, S. (2024). ROGUE WAVES IN DISCRETE KDV EQUATION. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 12(1), 55-61. https://doi.org/10.20290/estubtdb.1357676
AMA Tombuloğlu S. ROGUE WAVES IN DISCRETE KDV EQUATION. Estuscience - Theory. Şubat 2024;12(1):55-61. doi:10.20290/estubtdb.1357676
Chicago Tombuloğlu, Semiha. “ROGUE WAVES IN DISCRETE KDV EQUATION”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 12, sy. 1 (Şubat 2024): 55-61. https://doi.org/10.20290/estubtdb.1357676.
EndNote Tombuloğlu S (01 Şubat 2024) ROGUE WAVES IN DISCRETE KDV EQUATION. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 12 1 55–61.
IEEE S. Tombuloğlu, “ROGUE WAVES IN DISCRETE KDV EQUATION”, Estuscience - Theory, c. 12, sy. 1, ss. 55–61, 2024, doi: 10.20290/estubtdb.1357676.
ISNAD Tombuloğlu, Semiha. “ROGUE WAVES IN DISCRETE KDV EQUATION”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 12/1 (Şubat 2024), 55-61. https://doi.org/10.20290/estubtdb.1357676.
JAMA Tombuloğlu S. ROGUE WAVES IN DISCRETE KDV EQUATION. Estuscience - Theory. 2024;12:55–61.
MLA Tombuloğlu, Semiha. “ROGUE WAVES IN DISCRETE KDV EQUATION”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, c. 12, sy. 1, 2024, ss. 55-61, doi:10.20290/estubtdb.1357676.
Vancouver Tombuloğlu S. ROGUE WAVES IN DISCRETE KDV EQUATION. Estuscience - Theory. 2024;12(1):55-61.