Solitary wave solutions in two-Core optical fibers with coupling-coefficient dispersion and Kerr nonlinearity
DOI:
https://doi.org/10.31349/RevMexFis.67.369Keywords:
Two-core optical fiber, soliton solutions, Nonlinear Schrödinger equation.Abstract
In this paper, we studies chirped solitary waves in two-Core optical fibers with coupling-coefficient dispersion and intermodal dispersion. To construct chirp soliton, the couple of nonlinear Schrödinger equation which describing the pulses propagation along the two-core fiber have been reduced to one equivalent equation. By adopting the traveling-waves hypothesis, the exact analytical solutions of the GNSE were obtained by using three relevant mathematical methods namely the auxiliary equation method, the modified auxiliary equation method and the Sine-Gordon expansion approach. Lastly, the behavior of the chirped like-soliton solutions were discussed and some contours of the plot evolution of the bright and dark solitons are obtained.References
bibitem{R1}
Meltz, G., Dunphy, J. R., Morey, W. W., & Snitzer, E. (1983). {it Cross-talk fiber-optic temperature sensor}. Applied optics, 22(3), 464--477.
bibitem{R2}
Kartashov, Y. V., Vysloukh, V. A., & Torner, L. (2009). {it Soliton shape and mobility control in optical lattices}. Progress in Optics, 52, 63--148.
bibitem{R3}
Arshad, M., Seadawy, A. R., & Lu, D. (2017). {it Bright-dark solitary wave solutions of generalized higher-order nonlinear Schr"{o}dinger equation and its applications in optics}. Journal of Electromagnetic Waves and Applications, 31(16), 1711--1721.
bibitem{R4}
Kevrekidis, P. G., & Frantzeskakis, D. J. (2016). {it Solitons in coupled nonlinear Schr"{o}dinger models: a survey of recent developments}. Reviews in Physics, 1, 140--153.
bibitem{R5}
Biswas, A. (2012). {it Soliton solutions of the perturbed resonant nonlinear Schr"{o}dinger’s equation with full nonlinearity by semi-inverse variational principle}. Quantum Phys. Lett, 1(2), 79--89.
bibitem{R6}
Liu, M., & Shum, P. (2003). {it Generalized coupled nonlinear equations for the analysis of asymmetric two-core fiber coupler}. Optics express, 11(2), 116--119.
bibitem{R7}
Malomed, B. A., Skinner, I. M., & Tasgal, R. S. (1997). {it Solitons in a nonlinear optical coupler in the presence of the Raman effect}. Optics communications, 139(4-6), 247--251.
bibitem{R8}
Osman, M. S., Korkmaz, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., & Zhou, Q. (2018). {it The unified method for conformable time fractional Schr"{o}dinger equation with perturbation terms}. Chinese Journal of Physics, 56(5), 2500--2506.
bibitem{R88}
Osman, M. S., Rezazadeh, H., Eslami, M., Neirameh, A., & Mirzazadeh, M. (2018). {it Analytical study of solitons to benjamin-bona-mahony-peregrine equation with power law nonlinearity by using three methods}. Univ Politechnica Bucharest SciBull-Ser A-Appl Math Phys, 80(4), 267--278.
bibitem{R9}
Madji, H., Marhokh, A., M'{e}ndez, M.M. O., Arriaga, J., Iturbe, C. M. D. & Ch'{a}vez, C. S., (2019).{it Generation of Bright spatial quasi-solitons by arbitrary initial beam profiles in local andnonlocal (1+1)-Dimensional nonlinear media }. Optik,163695. doi:10.1016/j.ijleo.2019.163695.
bibitem{R99}
Biswas, A., Al-Amr, M. O., Rezazadeh, H., Mirzazadeh, M., Eslami, M., Zhou, Q., ... & Belic, M. (2018). {it Resonant optical solitons with dual-power law nonlinearity and fractional temporal evolution}. Optik, 165, 233--239.
bibitem{R10}
Majid, H., Mahrokh, A. & Mend'{e}z, M. M. O. (2019). {it Transforming higher order bright and dark solitons to the first order solitons in Kerr medium: A rewiev}. Optik, doi: https://doi.org/10.1016/j.ijleo.2019.163695.
bibitem{R100}
Eslami, M., Rezazadeh, H., Rezazadeh, M., & Mosavi, S. S. (2017). {it Exact solutions to the space-time fractional Schr"{o}dinger-Hirota equation and the space-time modified KDV-Zakharov-Kuznetsov equation}. Optical and Quantum Electronics, 49(8), 279.
bibitem{R11}
Rezazadeh, H. (2018). {it New solitons solutions of the complex Ginzburg-Landau equation with Kerr law nonlinearity}. Optik, 167, 218--227.
bibitem{R111}
Rezazadeh, H., Tariq, H., Eslami, M., Mirzazadeh, M., & Zhou, Q. (2018). {it New exact solutions of nonlinear conformable time-fractional Phi-4 equation}. Chinese Journal of Physics, 56(6), 2805--2816.
bibitem{R12}
Zhao, L. C., Li, S. C., & Ling, L. (2013). {it Rational W-shaped Optical Soliton on Continuous Wave in Presence of Kerr Dispersion and Stimulated Raman Scattering}. arXiv preprint arXiv:1310.7693.
bibitem{R13}
Snyder, A. W. (1972). {it Coupled-mode theory for optical fibers}. JOSA, 62(11), 1267--1277.
bibitem{R14}
Shamseldeen, S., Latif, M. S. A., Hamed, A., & Nour, H. (2017). {it New soliton solutions in dual-core optical fibers}. Communication in Mathematical Modeling and Applications, 2(2), 39--46.
bibitem{R15}
Wang, Z., Taru, T., Birks, T. A., Knight, J. C., Liu, Y., & Du, J. (2007). {it Coupling in dual-core photonic bandgap fibers: theory and experiment}. Optics express, 15(8), 4795--4803.
bibitem{R16}
Raju, T. S., Panigrahi, P. K., & Porsezian, K. (2005). {it Nonlinear compression of solitary waves in asymmetric twin-core fibers}. Physical Review E, 71(2), 026608.
bibitem{R17}
Younis, M., Rizvi, S. T. R., Zhou, Q., Biswas, A. N. J. A. N., & Belic, M. (2015). {it Optical solitons in dual-core fibers with G’/G-expansion scheme}. Journal of Optoelectronics and Advanced Materials, 17(3-4), 505--510.
bibitem{R18}
Wang, Z., Taru, T., Birks, T. A., Knight, J. C., Liu, Y., & Du, J. (2007). {it Coupling in dual-core photonic bandgap fibers: theory and experiment}. Optics express, 15(8), 4795--4803.
bibitem{R19}
Zhang, J., & Dai, C. (2005). {it Bright and dark optical solitons in the nonlinear Schr"{o}dinger equation with fourth-order dispersion and cubic-quintic nonlinearity}. Chinese Optics Letters, 3(5), 295--298.
bibitem{R20}
Alphonse, H., Hubert, M. B., Savaissou, N., Jerome, D., Justin, M., Betchewe, G., ... & Ekici, M. (2019). {it Optical solitons for higher-order nonlinear Schr"{o}dinger’s equation with three exotic integration architectures}. Optik, 179, 861--866.
bibitem{R21}
Khater, M., Attia, R., & Lu, D. (2019). {it Modified Auxiliary Equation Method versus Three Nonlinear Fractional Biological Models in Present Explicit Wave Solutions}. Mathematical and Computational Applications, 24(1), 1.
bibitem{R22}
Attia, R. A., Lu, D., & MA Khater, M. (2019). {it Chaos and relativistic energy-momentum of the nonlinear time fractional Duffing equation}. Mathematical and Computational Applications, 24(1), 10.
bibitem{R23}
Osman, M. S., Lu, D., Khater, M. M. A., & Attia, R. A. M. (2019). {it Complex wave structures for abundant solutions related to the complex Ginzburg-Landau model}. Optik, 192, 162927.
bibitem{R24}
Yan, C. (1996). {it A simple transformation for nonlinear waves}. Physics Letters A, 224(1-2), 77--84.
bibitem{R25}
Yan, Z., & Zhang, H. (1999). {it New explicit and exact travelling wave solutions for a system of variant Boussinesq equations in mathematical physics}. Physics Letters A, 252(6), 291--296.
bibitem{T1}
Li-Hua Z.(2009). {it Traveling-wave solution for the generalized Zakharov-Kuznetsov equation with higher-order nonlinear terms}. Appl. Math. Comp. 208, 144-155.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2021 Souleymanou Abbagari, Alphonse Houwe, Hadi Rezazadeh, Ahmet Bekir, Serge Y Doka
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
