Том 16, № 2Страницы 5 - 13 Exact Solutions of Beta-Fractional Fokas-Lenells Equation via Sine-Cosine Method
Volkan Ala, Berik RakhimzhanovВ нелинейной физике плазмы, фотонике и оптике пространственно-временное дробно-нелинейное уравнение Фокаса – Ленеллса, связанное с бета-производной, имеет важные приложения. В данной работе мы рассматриваем это уравнение для построения его точных решений методом синус-косинус. Кроме того, мы строим 2D-3D фигуры полученных решений в соответствии с подходящими параметрами с помощью компьютерного программного обеспечения. Из результатов следует, что предложенный метод прост, эффективен и способен генерировать исчерпывающие решения нелинейных моделей, возникающих в математической физике.
Полный текст- Ключевые слова
- уравнение Фокаса – Ленеллса; метод синус-косинус; бетапроизводная; точные решения.
- Литература
- 1. Adomian G. A Review of the Decomposition Method and Some Recent Results for Nonlinear Equations. Computers and Mathematics with Applications, 1991, vol. 21. no. 5, pp. 101-127. DOI: 10.1016/0898-1221(91)90220-X
2. Rezazadeh H. New Solitons Solutions of the Complex Ginzburg-Landau Equation with Kerr Law Nonlinearity. Optik - International Journal for Light and Electron Optics, 2018, vol. 167, pp. 218-227. DOI: 10.1016/j.ijleo.2018.04.026
3. Tala-Tebue E., Tsobgni-Fozap D.C., Kenfack-Jiotsa A., Kofane T.C. Envelope Periodic Solutions for a Discrete Network with the Jacobi Elliptic Functions and the Alternative (G^{\prime}/G)-Expansion Method Including the Generalized Riccati Equation. European Physical Journal Plus, 2014, vol. 129, no. 6, article ID: 136, 10 p. DOI: 10.1140/epjp/i2014-14136-9
4. Bekova G., Yesmakhanova K., Ozat N., Shaikhova G. Dark and Bright Solitons for the Two-Dimensional Complex Modified Korteweg-de Vries and Maxwell-Bloch System with Time-Dependent Coefficient. Journal of Physics: Conference Series. Prague, 2018, vol. 96, article ID: 012035, 10 p.
5. Yesmakhanova K., Bekova G., Shaikhova G., Myrzakulov R. Soliton Solutions of the (2+1)-Dimensional Complex Modified Korteweg-de Vries and Maxwell-Bloch Equations. Journal of Physics: Conference Series. Athens, 2016, vol. 738, article ID: 012018, 7 p. DOI: 10.1088/1742-6596/738/1/012018
6. Harivan R.N., Ismael H.F., Nehad A.S., Wajaree W. W-Shaped Soliton Solutions to the Modified Zakharov-Kuznetsov Equation of Ion-Acoustic Waves in (3+1)-Dimensions Arise in a Magnetized Plasma. AIMS Mathematics, 2023, vol. 8, no. 2, pp. 4467-4486. DOI: 10.3934/math.2023222
7. Baskonus H.M., Bulut H. Exponential Prototype Structures for (2+1)-Dimensional Boiti-Leon-Pempinelli Systems in Mathematical Physics. Waves in Random and Complex Media, 2016, vol. 26, no. 2, pp. 189-196. DOI: 10.1080/17455030.2015.1132860
8. Mamedov Kh.R., Demirbilek U., Ala V. Exact Solutions of the (2+1)-Dimensional Kundu-Mukherjee-Naskar Model via IBSEFM. Bulletin of the South Ural State University. Series: Mathematical Modelling, Programming and Computer Software, 2022, vol. 15, no. 2, pp. 17-26. DOI: 10.14529/mmp220202
9. Burdik C., Shaikhova G., Rakhimzhanov B. Soliton Solutions and Travelling Wave Solutions for the Two-Dimensional Generalized Nonlinear Schr"odinger Equations. European Physical Journal, 2021, vol. 136, no. 1095, pp. 1-17. DOI: 10.48550/arXiv.1909.00826
10. Shaikhova G., Kutum B., Myrzakulov R. Periodic Traveling Wave, Bright and Dark Soliton Solutions of the (2+1)-Dimensional Complex Modified Korteweg-de Vries System of Equations by Using Three Different Methods. AIMS Mathematics, 2022, vol. 7, no. 10, pp. 18948-18970. DOI: 10.3934/math.20221043
11. Ala V., Shaikhova G. Analytical Solutions of Nonlinear Beta Fractional Schr"odinger Equation via Sine-Cosine Method. Lobachevskii Journal of Mathematics, 2022, vol. 43, no. 11, pp. 3033-3038. DOI: 10.1134/S1995080222140025
12. Yesmakhanova K., Shaikhova G., Bekova G. Soliton Solutions of the Hirota's System. AIP Conference Proceedings. Almaty, 2016, vol. 1759, article ID: 020147, 5 p. DOI: 10.1063/1.4959761
13. El-Wakil S.A., Abdou M.A. New Exact Travelling Wave Solutions of Two Nonlinear Physical Models. Nonlinear Analysis, 2008, vol. 68, no. 2, pp. 235-245. DOI: 10.1016/j.na.2006.10.045
14. Zafar A., Raheel M., Bekir A., Razzaq W. The Conformable Space-Time Fractional Fokas-Lenells Equation and Its Optical Soliton Solutions Based on Three Analytical Schemes. International Journal of Modern Physics B, 2021, vol. 35, no. 1, article ID: 2150004, 16 p.
15. Biswas A., Ekici M., Sonmezoglu A., Alqahtani R.T. Optical Soliton Perturbation with Full Nonlinearity in Polarization Preserving Fibers Using Trial Equation Method. Journal of Optoelectronics and Advanced Materials, 2018, vol. 20, no. 7-8, pp. 385-402.
16. Biswas A., Yildirim Y., Yasar E., Triki H., Zhou Q., Moshokoa S.P., Belic M. Optical Solitons with Differential Group Delay for Coupled Fokas-Lenells Equation by Extended Trial Function Scheme. Optik - International Journal for Light and Electron Optics, 2018, vol. 165, pp. 102-110. DOI: 10.1016/j.ijleo.2018.03.102
17. Demiray S.T., Bulut H. New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas-Lenells Equation. Entropy, 2015, vol. 17, no. 9, pp. 6025-6043. DOI: 10.3390/e17096025
18. Ben-Hai Wang, Yue-Yue Wang, Chao-Qing Dai, Yi-Xiang Chen. Dynamical Characteristic of Analytical Fractional Solitons for the Space-Time Fractional Fokas-Lenells Equation. Alexandria Engineering Journal, 2020, vol. 59, no. 6, pp. 4699-4707. DOI: 10.1016/j.aej.2020.08.027
19. Sajid N., Akram G. Optical Solitons with Full Nonlinearity for the Conformable Space-Time Fractional Fokas-Lenells Equation. Optik - International Journal for Light and Electron Optics, 2019, vol. 196, article ID: 163131, 13 p. DOI: 10.1016/j.ijleo.2019.163131
20. Bulut H., Sulaiman T.A., Baskonus H.M., Rezazadeh H., Eslami M., Mirzazadeh M. Optical Solitons and Other Solutions to the Conformable Space-Time Fractional Fokas-Lenells Equation. Optik - International Journal for Light and Electron Optics, 2018, vol. 172, pp. 20-27. DOI: 10.1016/j.ijleo.2018.06.108
21. Sajid N., Akram G. Dark, Singular, Bright, Rational and Periodic Solutions of the Space-Time Fractional Fokas-Lenells Equation by the phi^6-Model Expansion. Optik - International Journal for Light and Electron Optics, vol. 228, article ID: 165843, 26 p. DOI: 10.1016/j.ijleo.2020.165843
22. Morshedul Haque Md., Akbar M.A., Osman M.S. Optical Soliton Solutions to the Fractional Nonlinear Fokas-Lenells and Paraxial Schr"odinger Equations. Optical and Quantum Electronics, 2022, vol. 54, article ID: 517. DOI: 10.1007/s11082-022-04145-1
23. Atangana A., Baleanu D. New Fractional Derivatives with Nonlocal and Non-Singular Kernel: Theory and Application to Heat Transfer Model. The Journal Thermal Science, 2016, vol. 20, pp. 763-769. DOI: 10.48550/arXiv.1602.03408
24. Wazwaz A.M. The Sine-Cosine Method for Obtaining Solutions with Compact and Noncompact Structures. Applied Mathematics and Computation, 2004, vol. 159, no. 2, pp. 559-576. DOI: 10.1016/j.amc.2003.08.136
25. Pashayi S., Hashemi M.S., Shahmorad S. Analytical Lie Group Approach for Solving Fractional Integro Differential Equations. Communications in Nonlinear Science and Numerical Simulation, 2017, vol. 51, pp. 66-77. DOI: 10.1016/j.cnsns.2017.03.023