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(2+1)- boyutlu Biswas-Milovic denkleminin modifiye edilmiş yeni Kudryashov yöntemi ile optik soliton çözümleri üzerine

Year 2023, Issue: 51, 14 - 20, 31.08.2023

Ramazan Tekercioğlu

https://doi.org/10.31590/ejosat.1141484

Abstract

Bu çalışma, optik fiberlerdeki soliton davranışını modelleyen önemli bir denklem olan, literature son zamanlarda sunulmuş olan (2+1) boyutlu Biswas-Milovic denkleminin optik soliton çözümlerinin incelenmesini içermektedir. İncelenen denklem ve yöntemin yakın zamanda tanıtılması ve çok fazla çalışma yapılmaması nedeniyle, modifiye edilmiş yeni Kudryashov yöntemi kullanılarak 3D, 2D ve kontur grafikleri desteklenerek çan şekli ve periyodik parlak optik soliton çözümleri elde edilmiş ve yorumlanmıştır.

Keywords

Biswas-Milovic denklemi Optik soliton Optik fiber Modifiye edilmiş yeni Kudryashov yaklaşımı

References

  • Alquran, Marwan, Qawasmeh, Aminah. (2014). Soliton solutions of shallow water wave equations by means of G'/G expansion method. Journal of Applied Analysis and Computation. 4. 10.11948/2014010.
  • Alphonse Houwe, Souleymanou Abbagari, Yakada Salathiel, Mustafa Inc, Serge Y. Doka, Kofane Timoléon Crépin, Dumitru Baleanu. Complex traveling-wave and solitons solutions to the Klein-Gordon-Zakharov equations, Results in Physics, Volume 17, 2020, 103127, ISSN 2211-3797, https://doi.org/10.1016/j.rinp.2020.103127.
  • Gia Dvali, Cesar Gomez, Lukas Gruending, Tehseen Rug. Towards a quantum theory of solitons, Nuclear Physics B, Volume 901, 2015, Pages 338-353, ISSN 0550-3213, https://doi.org/10.1016/j.nuclphysb.2015.10.017.
  • Yannis Kominis, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Dimitrios J. Frantzeskakis, Anastasios Bountis. Continuous families of solitary waves in non-symmetric complex potentials: A Melnikov theory approach, Chaos, Solitons & Fractals, Volume 118, 2019, Pages 222-233, ISSN 0960-0779, https://doi.org/10.1016/j.chaos.2018.11.021.
  • Zafar Asim, K. Ali Khalid, Raheel M., Jafar Numan, Nisar Kottakkaran. (2020). Soliton solutions to the DNA Peyrard-Bishop equation with beta-derivative via three distinctive approaches. European Physical Journal Plus. 135:726. 10.1140/epjp/s13360-020-00751-8.
  • I.S. Amiri, A. Afroozeh, I.N. Nawi, M.A. Jalil, A. Mohamad, J. Ali, P.P. Yupapin, Dark Soliton Array for Communication Security, Procedia Engineering, Volume 8, 2011, Pages 417-422, ISSN 1877-7058, https://doi.org/10.1016/j.proeng.2011.03.076.
  • Davies Elliot, Mocz, Philip. (2020). Fuzzy dark matter soliton cores around supermassive black holes. Monthly Notices of the Royal Astronomical Society. 492. 5721-5729. 10.1093/mnras/staa202.
  • Sekulić, Dalibor & Satarić, Miljko & Zivanov, Milos & Bajic, Jovan. (2012). Soliton-like Pulses along Electrical Nonlinear Transmission Line. Elektronika ir Elektrotechnika. 121. 53. 10.5755/j01.eee.121.5.1652.
  • Muslum Ozisik, Melih Cinar, Aydin Secer, Mustafa Bayram, Optical solitons with Kudryashov’s sextic power-law nonlinearity, Optik, Volume 261, 2022, 169202, ISSN 0030-4026, https://doi.org/10.1016/j.ijleo.2022.169202.
  • Muslum Ozisik, On the optical soliton solution of the (1+1)− dimensional perturbed NLSE in optical nano-fibers, Optik, Volume 250, Part 1, 2022, 168233, ISSN 0030-4026, https://doi.org/10.1016/j.ijleo.2021.168233.
  • Melih Cinar, Ismail Onder, Aydin Secer, Tukur Abdulkadir Sulaiman, Abdullahi Yusuf, Mustafa Bayram, (2021),Optical solitons of the (2+1)-dimensional Biswas–Milovic equation using modified extended tanh-function method, Optik, volume 245, 167631
  • Ozdemir, N., Esen, H., Secer, A., Bayram, M., Yusuf, A., Sulaiman, T. A., (2021),Optical Soliton Solutions to Chen Lee Liu model by the modified extended tanh expansion scheme, Optik, 245, 167643
  • Cinar, M., Onder, I., Secer, A., Yusuf, A., Sulaiman, T., Bayram, M., Aydın, H., (2021), Soliton Solutions of (2+ 1) Dimensional Heisenberg Ferromagnetic Spin Equation by the Extended Rational sine cosine and sinh cosh Method, International Journal of Applied and Computational Mathematics, 7(4)
  • Yıldırım Y., Topkara E., Biswas A., Triki H., Ekici M., Guggilla P., Khan S., R. Belic M., (2021), Cubic–quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by sine-Gordon equation approach. Journal of Optics (India), 50(2):322–329
  • Leonid L. F., (2021), Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations, Journal of Inverse and Ill-Posed Problems, v 29(3), pp. 369-383.
  • Ahmed H. Arnous, Anjan Biswas, Yakup Yıldırım, Qin Zhou, Wenjun Liu, Ali S. Alshomrani, Hashim M. Alshehri. Cubic–quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov’s method, Chaos, Solitons & Fractals, Volume 155, 2022, 111748, ISSN 0960-0779, https://doi.org/10.1016/j.chaos.2021.111748.
  • Zayed, E.M.E., Al-Nowehy, AG. The ϕ6-model expansion method for solving the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity. Opt Quant Electron 50, 164 (2018). https://doi.org/10.1007/s11082-018-1426-z.
  • Li-Na Gao, Xue-Ying Zhao, Yao-Yao Zi, Jun Yu, Xing Lü. Resonant behavior of multiple wave solutions to a Hirota bilinear equation, Computers & Mathematics with Applications, Volume 72, Issue 5, 2016, Pages 1225-1229, ISSN 0898-1221, https://doi.org/10.1016/j.camwa.2016.06.008.
  • Melih Cinar, Ismail Onder, Aydin Secer, Tukur Abdulkadir Sulaiman, Abdullahi Yusuf, Mustafa Bayram, (2021),Optical solitons of the (2+1)-dimensional Biswas–Milovic equation using modified extended tanh-function method, Optik, volume 245, 167631
  • Kudryashov, N. A., (2020), Method for finding highly dispersive optical solitons of nonlinear differential equations. Optik, 206:163550

On the optical soliton solutions of (2+1)-Biswas-Milovic equation via modified new Kudryashov method

Year 2023, Issue: 51, 14 - 20, 31.08.2023

Ramazan Tekercioğlu

https://doi.org/10.31590/ejosat.1141484

Abstract

This study includes the examination of optical soliton solutions of the (2+1)-dimensional Biswas-Milovic equation, which is an important equation modeling the soliton behavior in optical fibers, which has been introduced to the literature recently. Since the investigated equation and method are recently introduced and not much works has been done, the bell shape and periodic bright optical soliton solutions have been obtained and interpreted by supporting the 3D, 2D and contour graphics by utilizing the modified new Kudryashov method.

Keywords

Biswas-Milovic equation Optical soliton Optic fiber Modified new Kudryashov approach.

References

  • Alquran, Marwan, Qawasmeh, Aminah. (2014). Soliton solutions of shallow water wave equations by means of G'/G expansion method. Journal of Applied Analysis and Computation. 4. 10.11948/2014010.
  • Alphonse Houwe, Souleymanou Abbagari, Yakada Salathiel, Mustafa Inc, Serge Y. Doka, Kofane Timoléon Crépin, Dumitru Baleanu. Complex traveling-wave and solitons solutions to the Klein-Gordon-Zakharov equations, Results in Physics, Volume 17, 2020, 103127, ISSN 2211-3797, https://doi.org/10.1016/j.rinp.2020.103127.
  • Gia Dvali, Cesar Gomez, Lukas Gruending, Tehseen Rug. Towards a quantum theory of solitons, Nuclear Physics B, Volume 901, 2015, Pages 338-353, ISSN 0550-3213, https://doi.org/10.1016/j.nuclphysb.2015.10.017.
  • Yannis Kominis, Jesús Cuevas-Maraver, Panayotis G. Kevrekidis, Dimitrios J. Frantzeskakis, Anastasios Bountis. Continuous families of solitary waves in non-symmetric complex potentials: A Melnikov theory approach, Chaos, Solitons & Fractals, Volume 118, 2019, Pages 222-233, ISSN 0960-0779, https://doi.org/10.1016/j.chaos.2018.11.021.
  • Zafar Asim, K. Ali Khalid, Raheel M., Jafar Numan, Nisar Kottakkaran. (2020). Soliton solutions to the DNA Peyrard-Bishop equation with beta-derivative via three distinctive approaches. European Physical Journal Plus. 135:726. 10.1140/epjp/s13360-020-00751-8.
  • I.S. Amiri, A. Afroozeh, I.N. Nawi, M.A. Jalil, A. Mohamad, J. Ali, P.P. Yupapin, Dark Soliton Array for Communication Security, Procedia Engineering, Volume 8, 2011, Pages 417-422, ISSN 1877-7058, https://doi.org/10.1016/j.proeng.2011.03.076.
  • Davies Elliot, Mocz, Philip. (2020). Fuzzy dark matter soliton cores around supermassive black holes. Monthly Notices of the Royal Astronomical Society. 492. 5721-5729. 10.1093/mnras/staa202.
  • Sekulić, Dalibor & Satarić, Miljko & Zivanov, Milos & Bajic, Jovan. (2012). Soliton-like Pulses along Electrical Nonlinear Transmission Line. Elektronika ir Elektrotechnika. 121. 53. 10.5755/j01.eee.121.5.1652.
  • Muslum Ozisik, Melih Cinar, Aydin Secer, Mustafa Bayram, Optical solitons with Kudryashov’s sextic power-law nonlinearity, Optik, Volume 261, 2022, 169202, ISSN 0030-4026, https://doi.org/10.1016/j.ijleo.2022.169202.
  • Muslum Ozisik, On the optical soliton solution of the (1+1)− dimensional perturbed NLSE in optical nano-fibers, Optik, Volume 250, Part 1, 2022, 168233, ISSN 0030-4026, https://doi.org/10.1016/j.ijleo.2021.168233.
  • Melih Cinar, Ismail Onder, Aydin Secer, Tukur Abdulkadir Sulaiman, Abdullahi Yusuf, Mustafa Bayram, (2021),Optical solitons of the (2+1)-dimensional Biswas–Milovic equation using modified extended tanh-function method, Optik, volume 245, 167631
  • Ozdemir, N., Esen, H., Secer, A., Bayram, M., Yusuf, A., Sulaiman, T. A., (2021),Optical Soliton Solutions to Chen Lee Liu model by the modified extended tanh expansion scheme, Optik, 245, 167643
  • Cinar, M., Onder, I., Secer, A., Yusuf, A., Sulaiman, T., Bayram, M., Aydın, H., (2021), Soliton Solutions of (2+ 1) Dimensional Heisenberg Ferromagnetic Spin Equation by the Extended Rational sine cosine and sinh cosh Method, International Journal of Applied and Computational Mathematics, 7(4)
  • Yıldırım Y., Topkara E., Biswas A., Triki H., Ekici M., Guggilla P., Khan S., R. Belic M., (2021), Cubic–quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by sine-Gordon equation approach. Journal of Optics (India), 50(2):322–329
  • Leonid L. F., (2021), Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations, Journal of Inverse and Ill-Posed Problems, v 29(3), pp. 369-383.
  • Ahmed H. Arnous, Anjan Biswas, Yakup Yıldırım, Qin Zhou, Wenjun Liu, Ali S. Alshomrani, Hashim M. Alshehri. Cubic–quartic optical soliton perturbation with complex Ginzburg–Landau equation by the enhanced Kudryashov’s method, Chaos, Solitons & Fractals, Volume 155, 2022, 111748, ISSN 0960-0779, https://doi.org/10.1016/j.chaos.2021.111748.
  • Zayed, E.M.E., Al-Nowehy, AG. The ϕ6-model expansion method for solving the nonlinear conformable time-fractional Schrödinger equation with fourth-order dispersion and parabolic law nonlinearity. Opt Quant Electron 50, 164 (2018). https://doi.org/10.1007/s11082-018-1426-z.
  • Li-Na Gao, Xue-Ying Zhao, Yao-Yao Zi, Jun Yu, Xing Lü. Resonant behavior of multiple wave solutions to a Hirota bilinear equation, Computers & Mathematics with Applications, Volume 72, Issue 5, 2016, Pages 1225-1229, ISSN 0898-1221, https://doi.org/10.1016/j.camwa.2016.06.008.
  • Melih Cinar, Ismail Onder, Aydin Secer, Tukur Abdulkadir Sulaiman, Abdullahi Yusuf, Mustafa Bayram, (2021),Optical solitons of the (2+1)-dimensional Biswas–Milovic equation using modified extended tanh-function method, Optik, volume 245, 167631
  • Kudryashov, N. A., (2020), Method for finding highly dispersive optical solitons of nonlinear differential equations. Optik, 206:163550
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Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ramazan Tekercioğlu 0000-0003-2899-7386

Early Pub Date September 10, 2023
Publication Date August 31, 2023
Published in Issue Year 2023 Issue: 51

Cite

APA Tekercioğlu, R. (2023). On the optical soliton solutions of (2+1)-Biswas-Milovic equation via modified new Kudryashov method. Avrupa Bilim Ve Teknoloji Dergisi(51), 14-20. https://doi.org/10.31590/ejosat.1141484
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