Optical solitons and single traveling wave solutions of Biswas-Arshed equation in birefringent fibers with the beta-time derivative

Tianyong Han; Zhao Li; Jun Yuan; Tianyong Han; Zhao Li; Jun Yuan

doi:10.3934/math.2022837

AIMS Mathematics

2022, Volume 7, Issue 8: 15282-15297. doi: 10.3934/math.2022837

Previous Article Next Article

Research article Special Issues

Optical solitons and single traveling wave solutions of Biswas-Arshed equation in birefringent fibers with the beta-time derivative

1.
College of Computer Science, Chengdu University, Chengdu, Sichuan 610106, China
2.
School of Information Engineering, Nanjing Xiaozhuang University, Nanjing, Jiangsu 211171, China

Received: 11 April 2022 Revised: 24 May 2022 Accepted: 02 June 2022 Published: 17 June 2022
MSC : 35C05, 35Q55

This article describes the construction of optical solitons and single traveling wave solutions of Biswas-Arshed equation with the beta time derivative. By using the polynomial complete discriminant system method, a series of traveling wave solutions are constructed, including the rational function solutions, Jacobian elliptic function solutions, hyperbolic function solutions, trigonometric function solutions and inverse trigonometric function solutions. The conclusions of this paper comprise some new and different solutions that cannot be found in existing literature. Using the mathematic software Maple, the 3D and 2D graphs of the obtained traveling wave solutions were also developed. It is worth noting that these traveling wave solutions may motivate us to explore new phenomena which may be appear in optical fiber propagation theory.
- Biswas-Arshed equation with beta-time derivative,
- optical soliton,
- traveling wave solution,
- complete discrimination system method
Citation: Tianyong Han, Zhao Li, Jun Yuan. Optical solitons and single traveling wave solutions of Biswas-Arshed equation in birefringent fibers with the beta-time derivative[J]. AIMS Mathematics, 2022, 7(8): 15282-15297. doi: 10.3934/math.2022837

Related Papers:

Abstract

This article describes the construction of optical solitons and single traveling wave solutions of Biswas-Arshed equation with the beta time derivative. By using the polynomial complete discriminant system method, a series of traveling wave solutions are constructed, including the rational function solutions, Jacobian elliptic function solutions, hyperbolic function solutions, trigonometric function solutions and inverse trigonometric function solutions. The conclusions of this paper comprise some new and different solutions that cannot be found in existing literature. Using the mathematic software Maple, the 3D and 2D graphs of the obtained traveling wave solutions were also developed. It is worth noting that these traveling wave solutions may motivate us to explore new phenomena which may be appear in optical fiber propagation theory.

References

[1]	Y. Chalco-Cano, J. J. Nieto, A. Ouahab, H. Romn-Flores, Solution set for fractional differential equations with Riemann-Liouville derivative, Fract. Calc. Appl. Anal., 16(2013), 682–694. http://dx.doi.org/10.2478/s13540-013-0043-6 doi: 10.2478/s13540-013-0043-6
[2]	Y. G. Yan, Z. Z. Sun, J. W. Zhang, Fast evaluation of the Caputo fractional derivative and its applications to fractional diffusion equations: A second-order scheme, Commun. Comput. Phys., 22 (2017), 1028–1048. https://doi.org/10.4208/cicp.OA-2017-0019 doi: 10.4208/cicp.OA-2017-0019
[3]	R. Khalil, M. Al-Horani, A. Yousef, M. Sababheh, A new definition of fractional derivative, J. Comput. Appl. Math., 264(2014), 65–70. https://doi.org/10.1016/j.cam.2014.01.002 doi: 10.1016/j.cam.2014.01.002
[4]	A. Korkmaz, K. Hosseini, Exact solutions of a nonlinear conformable time-fractional parabolic equation with exponential nonlinearity using reliable methods, Opt. Quant. Electron., 49 (2017), Article number 278. https://doi.org/10.1007/s11082-017-1116-2 doi: 10.1007/s11082-017-1116-2
[5]	K. U. Tariq, M. Younis, H. Rezazadeh, et al, Optical solitons with quadratic-cubic nonlinearity and fractional temporal evolution, Mod. Phys. Lett. B, 32 (2018), Article number 1850317. https://doi.org/10.1142/S0217984918503177 doi: 10.1142/S0217984918503177
[6]	Z. Li, T. Y. Han, Bifurcation and exact solutions for the (2+1)-dimensional conformable time-fractional Zoomeron equation, Adv. Differ. Equ-Ny., 2020 (2020), Article number 656. https://doi.org/10.1186/s13662-020-03119-5 doi: 10.1186/s13662-020-03119-5
[7]	T. Y. Han, Z. Li, X. Zhang, Bifurcation and new exact traveling wave solutions to time-space coupled fractional nonlinear Schrodinger equation, Phys. Lett. A, 395 (2021), Article number 127217. https://doi.org/10.1016/j.physleta.2021.127217 doi: 10.1016/j.physleta.2021.127217
[8]	K. Hosseini, P. Mayeli, A. Bekir, O. Guner, D. O. Mathematics, R. Branch, Density-dependent conformable space-time fractional diffusion-reaction equation and its exact solutions, Commun. Theor. Phys., 69 (2018), 1–4. https://doi.org/10.1088/0253-6102/69/1/1 doi: 10.1088/0253-6102/69/1/1
[9]	T. Lu, S. P. Chen, The classication of single traveling wave solutions for the fractional coupled nonlinear Schrodinger equation, Opt. Quant. Electron., 54 (2022), Article number 105. https://doi.org/10.1007/s11082-021-03496-5 doi: 10.1007/s11082-021-03496-5
[10]	C. Huang, Z. Li, New Exact Solutions of the Fractional Complex Ginzburg-Landau Equation, Math. Probl. Eng., 2021 (2021), Article ID 1283083. https://doi.org/10.1155/2021/6640086 doi: 10.1155/2021/6640086
[11]	A. Biswas, M. O. Al-Amr, H. Rezazadeh, M. Mirzazadeh, M. Eslami, Q. Zhou, et al., Resonant optical solitons with dualpower law nonlinearity and fractional temporal evolution, Optik, 165 (2018), 233–239. https://doi.org/10.1016/j.ijleo.2018.03.123 doi: 10.1016/j.ijleo.2018.03.123
[12]	B. Ghanbari, J. F. Gómez-Aguilar, The generalized exponential rational function method for Radhakrishnan-Kundu-Lakshmanan equation with $\beta$-conformable time derivative, Revista Mexicana de Fsica, 65 (2019), 503–518. https://doi.org/10.31349/RevMexFis.65.503 doi: 10.31349/RevMexFis.65.503
[13]	A. Yusuf, M. Inc, A. I. Aliyu, D. Baleanu, Optical solitons possessing beta derivative of the Chen-Lee-Liu equation in optical fibers, Front. Phys., 7 (2019), Article number 34. https://doi.org/10.3389/fphy.2019.00034 doi: 10.3389/fphy.2019.00034
[14]	M. Fa. Uddin, M. G. Hafez, Z. Hammouch, D. Baleanu, Periodic and rogue waves for Heisenberg models of ferromagnetic spin chains with fractional beta derivative evolution and obliqueness, Waves Random Complex, 31 (2020), 2135–2149. https://doi.org/10.1080/17455030.2020.1722331 doi: 10.1080/17455030.2020.1722331
[15]	K. Hosseini, L. Kaur, M. Mirzazadeh, H. M. Baskonus, 1-Soliton solutions of the (2 + 1)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative, Opt. Quant. Electron., 53 (2021), Article number 125. https://doi.org/10.1007/s11082-021-02739-9 doi: 10.1007/s11082-021-02739-9
[16]	A. Zafar, A. Bekir, M. Raheel, K. Sooppy Nisar, S. Mustafa, Dynamics of new optical solitons for the Triki-Biswas model using beta-time derivative, Mod. Phys. Lett. B, 35 (2021), Article number 2150511. https://doi.org/10.1142/S0217984921505114 doi: 10.1142/S0217984921505114
[17]	S. T. Demiray, New Solutions of Biswas-Arshed Equation with Beta Time Derivative, Optik, 222 (2020), Article number 165405. https://doi.org/10.1016/j.ijleo.2020.165405 doi: 10.1016/j.ijleo.2020.165405
[18]	K. Hosseini, M. Mirzazadeh, M. Ilie, J. F. Gómez-Aguilar, Biswas-Arshed equation with the beta time derivative: Optical solitons and other solutions, Optik, 217 (2020), Article number 164801. https://doi.org/10.1016/j.ijleo.2020.164801 doi: 10.1016/j.ijleo.2020.164801
[19]	K. Khan, M. A. Akbar, Solitary and periodic wave solutions of nonlinear wave equations via the functional variable method, J. Interdiscip. Math., 21 (2018), 43–57. https://doi.org/10.1080/09720502.2014.962839 doi: 10.1080/09720502.2014.962839
[20]	K. Khan, M. A. Akbar, Solving unsteady Korteweg-de Vries equation and its two alternatives, Math. Method. Appl. Sci., 39 (2016), 2752–2760. https://doi.org/10.1002/mma.3727 doi: 10.1002/mma.3727
[21]	T. Y. Han, J. J. Wen, Z. Li, J. Yuan, New Traveling Wave Solutions for the (2+1)-Dimensional Heisenberg Ferromagnetic Spin Chain Equation, Math. Probl. Eng., 2022 (2022), Article ID 1312181, 9 pages. https://doi.org/10.1155/2022/1312181 doi: 10.1155/2022/1312181
[22]	T. Y. Han, J. J. Wen, Z. Li, Bifurcation Analysis and Single Traveling Wave Solutions of the Variable-Coefficient Davey-Stewartson System, Discrete Dyn. Nat. Soc., 2022 (2022), 1–6. https://doi.org/10.1155/2022/9230723 doi: 10.1155/2022/9230723
[23]	A. Biswas, S. Arshed, Optical solitons in presence of higher order dispersions and absence of self-phase modulation, Optik, 174 (2018), 452–459. https://doi.org/10.1016/j.ijleo.2018.08.037 doi: 10.1016/j.ijleo.2018.08.037
[24]	W. R. Xu, L. F. Guo, C. Y. Wang, Optical solutions of Biswas-Arshed equation in optical fibers, Mod. Phys. Lett. B, 35 (2021), Article number 2150051. https://doi.org/10.1142/S0217984921500512 doi: 10.1142/S0217984921500512
[25]	H. U. Rehman, S. Jafar, A. Javed, S. Hussain, M. Tahir, New optical solitons of Biswas-Arshed equation using different techniques, Optik, 206 (2019), Article number 163670. https://doi.org/10.1016/j.ijleo.2019.163670 doi: 10.1016/j.ijleo.2019.163670
[26]	N. Sajid, G. Akram, Novel solutions of Biswas-Arshed equation by newly $\Phi^6$ model expansion method, Optik, 211 (2020), Article number 164564. https://doi.org/10.1016/j.ijleo.2020.164564 doi: 10.1016/j.ijleo.2020.164564
[27]	Y. Yıldırım, Optical solitons with Biswas-Arshed equation by sine-Gordon equation method, Optik, 223 (2020), Article number 165622. https://doi.org/10.1016/j.ijleo.2020.165622 doi: 10.1016/j.ijleo.2020.165622
[28]	M. Tahir, A. U. Awan, Optical singular and dark solitons with Biswas-Arshed model by modified simple equation method, Optik, 202 (2020), Article number 163523. https://doi.org/10.1016/j.ijleo.2019.163523 doi: 10.1016/j.ijleo.2019.163523
[29]	A. Zafar, A. Bekir, M. Raheel, W. Razzaq, Optical soliton solutions to Biswas-Arshed model with truncated M-fractional derivative, Optik, 222 (2020), Article number 165355. https://doi.org/10.1016/j.ijleo.2020.165355 doi: 10.1016/j.ijleo.2020.165355
[30]	Y. Yıldırım, Optical solitons of Biswas-Arshed equation in birefringent fibers by trial equation technique, Optik, 182 (2019), 810–820. https://doi.org/10.1016/j.ijleo.2019.01.084 doi: 10.1016/j.ijleo.2019.01.084
[31]	M.M.A. El-Sheikh, H. M. Ahmed, A. H. Arnous, et al, Optical solitons and other solutions in birefringent fibers with Biswas-Arshed equation by Jacobi's elliptic function approach. Optik, 202 (2019), Article number 163546. https://doi.org/10.1016/j.ijleo.2019.163546 doi: 10.1016/j.ijleo.2019.163546
[32]	E. M. E. Zayed, R. M. A. Shohib, Optical solitons and other solutions to Biswas-Arshed equation using the extended simplest equation method, Optik, 185 (2019), 626–635. https://doi.org/10.1016/j.ijleo.2019.03.112 doi: 10.1016/j.ijleo.2019.03.112
[33]	A. Darwish, H. M. Ahmed, Ahmed H. Arnous, M. F. Shehab, Optical solitons of Biswas-Arshed equation in birefringent fibers using improved modified extended tanh-function method, Optik, 227 (2021), Article number 165385. https://doi.org/10.1016/j.ijleo.2020.165385 doi: 10.1016/j.ijleo.2020.165385
[34]	Z. Korpinar, M. Inc, M. Bayram, M. S. Hashemi, New optical solitons for Biswas-Arshed equation with higher order dispersions and full nonlinearity, Optik, 206 (2020), Article number 163332. https://doi.org/10.1016/j.ijleo.2019.163332 doi: 10.1016/j.ijleo.2019.163332
[35]	P. K. Das, Chirped and chirp-free optical exact solutions of the Biswas-Arshed equation with full nonlinearity by the rapidly convergent approximation method, Optik, 223(2020), Article number 165293. https://doi.org/10.1016/j.ijleo.2020.165293 doi: 10.1016/j.ijleo.2020.165293
[36]	H. U. Rehman, M. S. Saleem, M.Zubair, S. Jafar, I. Latif, Optical solitons with Biswas-Arshed model using mapping method, Optik, 194 (2019), Article number 163091. https://doi.org/10.1016/j.ijleo.2019.163091 doi: 10.1016/j.ijleo.2019.163091
[37]	N. A. Kudryashov, Periodic and solitary waves of the Biswas-Arshed equation, Optik, 200 (2020), Article number 163442. https://doi.org/10.1016/j.ijleo.2019.163442 doi: 10.1016/j.ijleo.2019.163442
[38]	H. U. Rehman, M. Tahir, M. Bibi, Z. Ishfaq, Optical solitons to the Biswas-Arshed model in birefringent fibers using couple of integration techniques, Optik, 218 (2020), Article number 164894. https://doi.org/10.1016/j.ijleo.2020.164894 doi: 10.1016/j.ijleo.2020.164894
[39]	M. Munawar, A. Jhangeer, A. Pervaiz, F. Ibraheem, New general extended direct algebraic approach for optical solitons of Biswas-Arshed equation through birefringent fibers, Optik, 228 (2021), Article number 165790. https://doi.org/10.1016/j.ijleo.2020.165790 doi: 10.1016/j.ijleo.2020.165790
[40]	N. A. Kudryashov, Solitary wave solutions of the generalized Biswas-Arshed equation, Optik, 219(2020), Article number 165002. https://doi.org/10.1016/j.ijleo.2020.165002 doi: 10.1016/j.ijleo.2020.165002
[41]	L. Tang, Exact solutions to conformable time-fractional Klein-Gordon equation with high-order nonlinearities. Results Phys., 18 (2020), Article number 103289. https://doi.org/10.1016/j.rinp.2020.103289 doi: 10.1016/j.rinp.2020.103289
[42]	A. Atangana, R. T. Alqahtani, Modelling the spread of river blindness disease via the Caputo fractional derivative and the beta-derivative, Entropy, 18 (2016), Article number 40. https://doi.org/10.3390/e18020040 doi: 10.3390/e18020040

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)