(2+1)-Boyutlu Kundu-Mukherjee-Naskar Denkleminin Birle¸sik Çözücü Teknik Yoluyla Dark ve Bright Solitonlarının Incelenmesi

Öz

Bu çalışmada, (2+1)-boyutlu Kundu-Mukherjee-Naskar denkleminin dark ve bright soliton çözümleri varyasyonel metot aracılığıyla birleştirilmiş çözücü teknikle inşa edilmiştir. tekniğin temel özelliklerine uygun olarak dark ve bright soliton çözümleri elde edilmiştir. Ayrıca elde edilen çözümlere spesifik değerler verilerek, çözümlerin iki ve üç boyutlu grafikleri paket program aracılığıyla çizilmiştir. Birleşik çözüm tekniği, akışkanlar mekaniği, nükleer, plazma ve parçacık fiziğindeki kısmi diferansiyel denklemlerin çeşitli tam çözümlerini elde etmek için uygulanabilen kullanımı kolay bir yöntemdir.

Anahtar Kelimeler

• Dalga dönüşümü
• birleştirilmiş çözücü teknik
• solitonlar

Examination of dark and bright solitons of (2+1)-dimensional Kundu-Mukherjee-Naskar equation via unified solver technique

Öz

In this study, dark and bright solitons of the (2+1)-dimensional Kundu-Mukherjee-Naskar equation are constructed with unified solver in terms of He's variations method. In accordance with basic properties of proposed technique, some dark and bright solitons are obtained. Moreover, giving specific values to the achieved solutions, 2D and 3D graphics are plotted with the help of software package.The unified solver technique extract vital solutions in explicit way. It is an easy-to-use method applied to obtain various exact solutions of nonlinear partial differential equations arising in fluid mechanics, nuclear, plasma and particle physics.

Anahtar Kelimeler

• Wave transformation
• unified solver technique
• solitons

Kaynakça

1. Doran, N., & Blow, K. (1983). Solitons in optical communications. IEEE Journal of Quantum Electronics, 19(12), 1883-1888. https://doi.org/10.1109/JQE.1983.1071806
2. Haus, H. A., & Wong, W. S. (1996). Solitons in optical communications. Reviews of Modern Physics, 68(2), 423-444. https://doi.org/10.1103/RevModPhys.68.423
3. Ata¸s, S. S., Ali, K. K., Sulaiman, T.A., & Bulut, H. (2022). Optical solitons to the Fokas system equation in monomode optical fibers. Optical and Quantum Electronics, 54(11), 1-13. https://doi.org/10.1007/s11082-022-04120-w
4. Başkonuş, H. M., Sulaiman, T. A., & Bulut, H. (2018). Dark, bright and other optical solitons to the decoupled nonlinear Schrödinger equation arising in dual-core optical fibers. Optical and Quantum Electronics, 50, Article 165. https://doi.org/10.1007/s11082-018-1433-0
5. Al-Ghafri, K., Krishnan, E., & Biswas, A. (2021).W-shaped and other solitons in optical nanofibers. Results in Physics, 23, Article 103973. https://doi.org/10.1016/j.rinp.2021.103973
6. Kundu, A., & Mukherjee A. (2013). Novel integrable higher-dimensional nonlinear Schroedinger equation: properties, solutions, applications. arXiv:1305.4023v1 [nlinSI] https://doi.org/10.48550/arXiv.1305.4023
7. Kundu A, Mukherjee A, & Naskar T. (2014). Modelling rogue waves through exact dynamical lump soliton controlled by ocean currents. Proceedings of the Royal Society A-Math Phy., 470(2164), 1-20. https://doi.org/10.1098/rspa.2013.0576
8. Mukherjee, A., & Kundu, A. (2019). Novel nonlinear wave equation: Regulated rogue waves and accelerated soliton solutions. Physics Letters A, 383(10), 985-990. https://doi.org/10.1016/j.physleta.2018.12.023

9. Mukherjee, A., Janaki, M., & Kundu, A. (2019). A new (2+1)-dimensional integrable evolution equation for an ion acoustic wave in a magnetized plasma. Physics of Plasmas, 22, Article 072302. https://doi.org/10.1063/1.4923296
10. Biswas, A., Vega-Guzman, J., Bansal, A., Kara, A. H., Alzahrani, A. K., Zhou, Q., & Belic, M. R. (2020). Optical dromions, domain walls and conservation laws with Kundu-Mukherjee-Naskar equation via traveling waves and Lie symmetry. Results in Physics, 16, 102850. https://doi.org/10.1016/j.rinp.2019.102850
11. Yıldırım, Y., & Mirzazadeh, M. (2019). Optical pulses with Kundu-Mukherjee-Naskar model in fiber communication systems. Chinese Journal of Physics, 64, 183-193. https://doi.org/10.1016/j.cjph.2019.10.025
12. Yıldırım, Y. (2019). Optical solitons to Kundu–Mukherjee–Naskar model with trial equation approach. Optik, 183, 1061–1065. https://doi.org/10.1016/j.ijleo.2019.02.117
13. Rizvi, S. T. R., Afzal, I., & Ali, K. (2020). Dark and singular optical solitons for Kundu-Mukherjee-Naskar model. Modern Physics Letters B, 34(6), 1-9. https://doi.org/10.1142/S0217984920500748
14. Al-Ghafri, K. S. (2021). Soliton structures in optical fiber communications with Kundu–Mukherjee–Naskar model. Open Physics, 19, 679-682. https://doi.org/10.1515/phys-2021-0074
15. Mamedov, K. R., Demirbilek, U., & Ala, V. (2022). Exact solutions of the (2+1)-dimensional Kundu–Mukherjee–Naskar Model via IBSEFM. Bulletin of the South Ural State University Series, Mathematical Modelling, Programming, Computer Software, 15(2), 17–26. https://doi.org/10.14529/mmp220202
16. Önder, I., Seçer, A., Özışık, M., & Bayram, M. (2022). On the optical soliton solutions of Kundu–Mukherjee–Naskar equation via two different analytical methods. Optik, 257, Article 168761. https://doi.org/10.1016/j.ijleo.2022.168761
17. Kumar, D., Paul, G. C., Biswas, T., Seadawy, A. R., Baowali, R., Kamal, M., & Rezazadeh, H. (2020). Optical solutions to the Kundu-Mukherjee-Naskar equation: mathematical and graphical analysis with oblique wave propagation. Physica Scripta, 96(2), Article 025218. https://doi.org/10.1088/1402-4896/abd201
18. Günerhan H., Khodadad F. S., Rezazadeh H., & Khate, M. M. A. (2020). Exact optical solutions of the (2+1) dimensions Kundu–Mukherjee–Naskar model via the new extended direct algebraic method. Modern Physics Letters B, 34(22), Article 2050225. https://doi.org/10.1142/S0217984920502255
19. Kudryashov, N. A. (2019). General solution of traveling wave reduction for the Kundu–Mukherjee–Naskar model. Optik, 186, 22-27. https://doi.org/10.1016/j.ijleo.2019.04.072
20. Petrovic, N. (2022). Chirped solitary and traveling wave solutions for the Kundu–Mukherjee–Naskar equation using the Jacobi elliptic function expansion method. Optical and Quantum Electronics, 54(10), 1–8. https://doi.org/10.1007/s11082-022-04024-9
21. Ekici M., Sönmezoğlu A., Biswas A., & Belic, M. R. (2019). Optical Solitons in (2+1)-Dimensions with Kundu–Mukherjee–Naskar Equation by Extended Trial Function Scheme. Chinese Journal of Physics, 57, 72-77. https://doi.org/10.1016/j.cjph.2018.12.011
22. Rezazadeh, H., Kurt A., Tozar A., Tasbozan, O., & Mirhosseini-Alizamini, S. M. (2021). Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure. Optical and Quantum Electronics, 53, Article 317. https://doi.org/10.1007/s11082-021-02926-8
23. Çakıcıoğlu, H., Çınar M., Seçer A., & Bayram, M. (2023). Optical solitons for Kundu–Mukherjee–Naskar equation via enhanced modified extended tanh method. Optical and Quantum Electronics, 55, Article 400. http://doi.org/10.1007/s11082-023-04686-z
24. Mohammed, W. W., Al-Askar, F. M., Cesarano, C., & El-Morshedy, M. (2022). The optical solutions of the stochastic fractional Kundu–Mukherjee–Naskar Model by Two Different Methods. Mathematics, 10(9), Article 1465. https://doi.org/10.3390/math10091465
25. He, J. (1997). Semi-inverse method of establishing generalized variational principles for fluid mechanics with emphasis on turbo machinery aerodynamics. International Journal of Turbo and Jet Engines, 14, 23-28. https://doi.org/10.1515/TJJ.1997.14.1.23
26. He, J. (2006). Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B, 20, 1141-1199. https://doi.org/10.1142/S0217979206033796
27. Kudryashov, N. (2009). Seven common errors in finding exact solutions of nonlinear differential equations. Communications in Nonlinear Science and Numerical Simulation, 14(9-10), 3507-3529. https://doi.org/10.1016/j.cnsns.2009.01.023