Mots-clés : exact solutions, Fokas–Lenells equation.
@article{VYURU_2023_16_2_a0,
author = {Volkan Ala and Berik Rakhimzhanov},
title = {Exact solutions of beta-fractional {Fokas{\textendash}Lenells} equation via sine-cosine method},
journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
pages = {5--13},
year = {2023},
volume = {16},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VYURU_2023_16_2_a0/}
}
TY - JOUR AU - Volkan Ala AU - Berik Rakhimzhanov TI - Exact solutions of beta-fractional Fokas–Lenells equation via sine-cosine method JO - Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie PY - 2023 SP - 5 EP - 13 VL - 16 IS - 2 UR - http://geodesic.mathdoc.fr/item/VYURU_2023_16_2_a0/ LA - en ID - VYURU_2023_16_2_a0 ER -
%0 Journal Article %A Volkan Ala %A Berik Rakhimzhanov %T Exact solutions of beta-fractional Fokas–Lenells equation via sine-cosine method %J Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie %D 2023 %P 5-13 %V 16 %N 2 %U http://geodesic.mathdoc.fr/item/VYURU_2023_16_2_a0/ %G en %F VYURU_2023_16_2_a0
Volkan Ala; Berik Rakhimzhanov. Exact solutions of beta-fractional Fokas–Lenells equation via sine-cosine method. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 16 (2023) no. 2, pp. 5-13. http://geodesic.mathdoc.fr/item/VYURU_2023_16_2_a0/
[1] Adomian G., “A Review of the Decomposition Method and Some Recent Results for Nonlinear Equations”, Computers and Mathematics with Applications, 21:5 (1991), 101–127 | DOI | MR | Zbl
[2] Rezazadeh H., “New Solitons Solutions of the Complex Ginzburg–Landau Equation with Kerr Law Nonlinearity”, Optik – International Journal for Light and Electron Optics, 167 (2018), 218–227 | DOI
[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, 129:6 (2014), 136, 10 pp. | DOI
[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” (Prague), Journal of Physics: Conference Series, 96 (2018), 012035, 10 pp.
[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” (Athens), Journal of Physics: Conference Series, 738 (2016), 012018, 7 pp. | DOI
[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, 8:2 (2023), 4467–4486 | DOI | MR
[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, 26:2 (2016), 189–196 | DOI | MR | Zbl
[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, 15:2 (2022), 17–26 | DOI | MR | Zbl
[9] Burdik C., Shaikhova G., Rakhimzhanov B., “Soliton Solutions and Travelling Wave Solutions for the Two-Dimensional Generalized Nonlinear Schrödinger Equations”, European Physical Journal, 136:1095 (2021), 1–17 | DOI
[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, 7:10 (2022), 18948–18970 | DOI | MR
[11] Ala V., Shaikhova G., “Analytical Solutions of Nonlinear Beta Fractional Schrödinger Equation via Sine-Cosine Method”, Lobachevskii Journal of Mathematics, 43:11 (2022), 3033–3038 | DOI | MR
[12] Yesmakhanova K., Shaikhova G., Bekova G., “Soliton Solutions of the Hirota's System” (Almaty), AIP Conference Proceedings, 1759 (2016), 020147, 5 pp. | DOI
[13] El-Wakil S.A., Abdou M.A., “New Exact Travelling Wave Solutions of Two Nonlinear Physical Models”, Nonlinear Analysis, 68:2 (2008), 235–245 | DOI | MR | Zbl
[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, 35:1 (2021), 2150004, 16 pp. | DOI | MR | Zbl
[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, 20:7–8 (2018), 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, 165 (2018), 102–110 | DOI | MR
[17] Demiray S.T., Bulut H., “New Exact Solutions of the New Hamiltonian Amplitude-Equation and Fokas–Lenells Equation”, Entropy, 17:9 (2015), 6025–6043 | DOI | MR | Zbl
[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, 59:6 (2020), 4699–4707 | DOI
[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, 196 (2019), 163131, 13 pp. | DOI
[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, 172 (2018), 20–27 | DOI
[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, 228 (1658), 43, 26 pp. | DOI
[22] Morshedul Haque Md., Akbar M.A., Osman M.S., “Optical Soliton Solutions to the Fractional Nonlinear Fokas–Lenells and Paraxial Schrödinger Equations”, Optical and Quantum Electronics, 54 (2022), 517 | DOI
[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, 20 (2016), 763–769 | DOI
[24] Wazwaz A.M., “The Sine-Cosine Method for Obtaining Solutions with Compact and Noncompact Structures”, Applied Mathematics and Computation, 159:2 (2004), 559–576 | DOI | MR | Zbl
[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, 51 (2017), 66–77 | DOI | MR | Zbl