KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI

Semiha Tombuloğlu

doi:10.20290/estubtdb.636310

Research Article

KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI

Year 2020, Volume: 8 Issue: 1, 99 - 104, 28.02.2020

Semiha Tombuloğlu

https://doi.org/10.20290/estubtdb.636310

Abstract

Rogue dalgaları, deniz yüzeyinde
birdenbire beliren ve hızla kaybolan dalgalardır. Genlikleri geri kalan deniz
yüzeyinden en az iki kat daha yüksektir. Birçok farklı fiziksel alanda
gözlenebilir olması sebebiyle önemlidir. Bu çalışmamızda, bir boyutlu lineer
olmayan kesikli Schrödinger (DNLS) denklemini belirli başlangıç koşulunda ve
periyodik sınır koşulları altında nümerik olarak çözdük. Başlangıç koşulundaki
katsayılar arasında belirli bir oran olduğunda üçlü rogue dalgası elde edileceğini
gösterdik. Seçilen başlangıç koşulundaki katsayıların değişiminin rogue dalga
dinamiğini önemli derecede etkilediğini ortaya koyduk.

Keywords

Rogue dalgaları, kesikli lineer olmayan Schrödinger denklemi, üçlü rogue dalgası

References

[1] E. Pelinovsky • C. Kharif, Extreme Ocean waves, vol. 8380. Springer, 2008.
[2] C. Kharif and E. Pelinovsky, “Physical mechanisms of the rogue wave phenomenon,” Eur. J. Mech., vol. 22, no. 6, pp. 603–634, 2003.
[3] K. Dysthe, H. E. Krogstad, and P. Müller, “Oceanic rogue waves,” Annu. Rev. Fluid Mech., vol. 40, pp. 287–310, 2008.
[4] M. P. Tulin and T. Waseda, Laboratory observations of wave group evolution, including breaking effects, vol. 378. 1999.
[5] A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett., vol. 106, no. 20, p. 204502, 2011.
[6] L. Wen, L. Li, Z.-D. Li, S.-W. Song, X.-F. Zhang, and W. M. Liu, “Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction,” Eur. Phys. J. D, vol. 64, no. 2–3, pp. 473–478, 2011.
[7] W. M. Moslem, “Langmuir rogue waves in electron-positron plasmas,” Phys. Plasmas, vol. 18, no. 3, p. 32301, 2011.
[8] M. M. Selim, H. G. Abdelwahed, and M. A. El-Attafi, “Nonlinear dust acoustic rogue waves in a two temperature charged dusty grains plasma,” Astrophys. Space Sci., vol. 359, no. 1, 2015.
[9] Y. Zhen-Ya, “Financial rogue waves,” Commun. Theor. Phys., vol. 54, no. 5, p. 947, 2010.
[10] T. Waseda, T. Kinoshita, and H. Tamura, “Evolution of a random directional wave and freak wave occurrence,” J. Phys. Oceanogr., vol. 39, no. 3, pp. 621–639, 2009.
[11] D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” J. Aust. Math. Soc. Ser. B. Appl. Math., vol. 25, no. 01, p. 16, 1983.
[12] V. I. Shrira and V. V Geogjaev, “What makes the Peregrine soliton so special as a prototype of freak waves?,” J. Eng. Math., vol. 67, no. 1–2, pp. 11–22, 2010.
[13] N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, “Extreme waves that appear from nowhere: on the nature of rogue waves,” Phys. Lett. A, vol. 373, no. 25, pp. 2137–2145, 2009.
[14] B. Kibler et al., “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys., vol. 6, no. 10, p. 790, 2010.
[15] V. E. Zakharovand and A. B. Shabat, “Exact Theory of Two-Dimensional Self-Focusing and One- Dimensional Self-Modulation of Waves in Nonlinear Media,” Zh. Eksp. Teor. Fiz, vol. 34, no. 61, pp. 118–134, 1972.
[16] M. J. Ablowitz, B. Prinari, and A. D. Trubatch, “Discrete and continuous nonlinear Schr¨ odinger systems,” October, vol. 43, no. 1, pp. 127–132, 2004.
[17] Y. V Bludov, V. V Konotop, and N. Akhmediev, “Rogue waves as spatial energy concentrators in arrays of nonlinear waveguides.,” Opt. Lett., vol. 34, no. 19, pp. 3015–7, 2009.
[18] S. Efe and C. Yuce, “Discrete rogue waves in an array of waveguides,” Phys. Lett. Sect. A Gen. At. Solid State Phys., vol. 379, no. 18–19, pp. 1251–1255, 2015.
[19] A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. Sect. A Gen. At. Solid State Phys., vol. 375, no. 28–29, pp. 2782–2785, 2011.

Year 2020, Volume: 8 Issue: 1, 99 - 104, 28.02.2020

Semiha Tombuloğlu

https://doi.org/10.20290/estubtdb.636310

Abstract

References

[1] E. Pelinovsky • C. Kharif, Extreme Ocean waves, vol. 8380. Springer, 2008.
[2] C. Kharif and E. Pelinovsky, “Physical mechanisms of the rogue wave phenomenon,” Eur. J. Mech., vol. 22, no. 6, pp. 603–634, 2003.
[3] K. Dysthe, H. E. Krogstad, and P. Müller, “Oceanic rogue waves,” Annu. Rev. Fluid Mech., vol. 40, pp. 287–310, 2008.
[4] M. P. Tulin and T. Waseda, Laboratory observations of wave group evolution, including breaking effects, vol. 378. 1999.
[5] A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, “Rogue wave observation in a water wave tank,” Phys. Rev. Lett., vol. 106, no. 20, p. 204502, 2011.
[6] L. Wen, L. Li, Z.-D. Li, S.-W. Song, X.-F. Zhang, and W. M. Liu, “Matter rogue wave in Bose-Einstein condensates with attractive atomic interaction,” Eur. Phys. J. D, vol. 64, no. 2–3, pp. 473–478, 2011.
[7] W. M. Moslem, “Langmuir rogue waves in electron-positron plasmas,” Phys. Plasmas, vol. 18, no. 3, p. 32301, 2011.
[8] M. M. Selim, H. G. Abdelwahed, and M. A. El-Attafi, “Nonlinear dust acoustic rogue waves in a two temperature charged dusty grains plasma,” Astrophys. Space Sci., vol. 359, no. 1, 2015.
[9] Y. Zhen-Ya, “Financial rogue waves,” Commun. Theor. Phys., vol. 54, no. 5, p. 947, 2010.
[10] T. Waseda, T. Kinoshita, and H. Tamura, “Evolution of a random directional wave and freak wave occurrence,” J. Phys. Oceanogr., vol. 39, no. 3, pp. 621–639, 2009.
[11] D. H. Peregrine, “Water waves, nonlinear Schrödinger equations and their solutions,” J. Aust. Math. Soc. Ser. B. Appl. Math., vol. 25, no. 01, p. 16, 1983.
[12] V. I. Shrira and V. V Geogjaev, “What makes the Peregrine soliton so special as a prototype of freak waves?,” J. Eng. Math., vol. 67, no. 1–2, pp. 11–22, 2010.
[13] N. Akhmediev, J. M. Soto-Crespo, and A. Ankiewicz, “Extreme waves that appear from nowhere: on the nature of rogue waves,” Phys. Lett. A, vol. 373, no. 25, pp. 2137–2145, 2009.
[14] B. Kibler et al., “The Peregrine soliton in nonlinear fibre optics,” Nat. Phys., vol. 6, no. 10, p. 790, 2010.
[15] V. E. Zakharovand and A. B. Shabat, “Exact Theory of Two-Dimensional Self-Focusing and One- Dimensional Self-Modulation of Waves in Nonlinear Media,” Zh. Eksp. Teor. Fiz, vol. 34, no. 61, pp. 118–134, 1972.
[16] M. J. Ablowitz, B. Prinari, and A. D. Trubatch, “Discrete and continuous nonlinear Schr¨ odinger systems,” October, vol. 43, no. 1, pp. 127–132, 2004.
[17] Y. V Bludov, V. V Konotop, and N. Akhmediev, “Rogue waves as spatial energy concentrators in arrays of nonlinear waveguides.,” Opt. Lett., vol. 34, no. 19, pp. 3015–7, 2009.
[18] S. Efe and C. Yuce, “Discrete rogue waves in an array of waveguides,” Phys. Lett. Sect. A Gen. At. Solid State Phys., vol. 379, no. 18–19, pp. 1251–1255, 2015.
[19] A. Ankiewicz, D. J. Kedziora, and N. Akhmediev, “Rogue wave triplets,” Phys. Lett. Sect. A Gen. At. Solid State Phys., vol. 375, no. 28–29, pp. 2782–2785, 2011.

There are 19 citations in total.

Details

Primary Language	Turkish
Journal Section	Articles
Authors	Semiha Tombuloğlu 0000-0003-2273-5633
Publication Date	February 28, 2020
Published in Issue	Year 2020 Volume: 8 Issue: 1

Cite

APA	Tombuloğlu, S. (2020). KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, 8(1), 99-104. https://doi.org/10.20290/estubtdb.636310
AMA	Tombuloğlu S. KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. February 2020;8(1):99-104. doi:10.20290/estubtdb.636310
Chicago	Tombuloğlu, Semiha. “KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler 8, no. 1 (February 2020): 99-104. https://doi.org/10.20290/estubtdb.636310.
EndNote	Tombuloğlu S (February 1, 2020) KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 8 1 99–104.
IEEE	S. Tombuloğlu, “KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI”, Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler, vol. 8, no. 1, pp. 99–104, 2020, doi: 10.20290/estubtdb.636310.
ISNAD	Tombuloğlu, Semiha. “KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI”. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler 8/1 (February 2020), 99-104. https://doi.org/10.20290/estubtdb.636310.
JAMA	Tombuloğlu S. KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2020;8:99–104.
MLA	Tombuloğlu, Semiha. “KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI”. Eskişehir Teknik Üniversitesi Bilim Ve Teknoloji Dergisi B - Teorik Bilimler, vol. 8, no. 1, 2020, pp. 99-104, doi:10.20290/estubtdb.636310.
Vancouver	Tombuloğlu S. KESİKLİ DOĞRUSAL OLMAYAN SCHRÖDİNGER DENKLEMİNDE ÜÇLÜ ROGUE DALGALARI. Eskişehir Teknik Üniversitesi Bilim ve Teknoloji Dergisi B - Teorik Bilimler. 2020;8(1):99-104.