Solitary wave solutions in two-Core optical fibers with coupling-coefficient dispersion and Kerr nonlinearity

Authors

  • S. Abbagari University of Maroua
  • A. Houwe University of Maroua
  • H. Rezazadeh Amol University of Special Modern Technologies
  • A. Bekir Eskisehir http://orcid.org/0000-0001-9394-4681
  • S. Y. Doka The University of Ngaoundere

DOI:

https://doi.org/10.31349/RevMexFis.67.369

Keywords:

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.

Author Biography

A. Bekir, Eskisehir

Ahmet Bekir currently works at Eskisehir. His research interests are theory and exact solutions of partial differential equations in mathematical physics. His favourites in mathematics are ODEs, PDEs, fractional differential equations, integral equations and analytic methods. He has published more than 200 articles journals.

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

2021-05-01

How to Cite

[1]
S. Abbagari, A. Houwe, H. Rezazadeh, A. Bekir, and S. Y. Doka, “Solitary wave solutions in two-Core optical fibers with coupling-coefficient dispersion and Kerr nonlinearity”, Rev. Mex. Fís., vol. 67, no. 3 May-Jun, pp. 369–377, May 2021.

Issue

Section

07 Gravitation, Mathematical Physics and Field Theory