Journal of Physical Studies 25(2), Article 2001 [10 pages] (2021) DOI: https://doi.org/10.30970/jps.25.2001 OPTICAL SOLITON PERTURBATION AND POLARIZATION WITH QUADRATIC–CUBIC NONLINEARITY BY SINE-GORDON EQUATION APPROACH Y. Yıldırım{1} , E. Topkara{2}, A. Biswas{3,4,5,6} , H. Triki{7}, M. Ekici8, P. Guggilla3, S. Khan3 , M. R. Belic9 1Department of Mathematics, Faculty of Arts and Sciences, Near East University, 99138 Nicosia, Cyprus 2Department of Mathematics, Huston–Tillotson University, Austin, TX–78702, USA 3Department of Physics, Chemistry and Mathematics, Alabama A\&M University, Normal, AL 35762–4900, USA 4Mathematical Modeling and Applied Computation (MMAC) Research Group, Department of Mathematics, King Abdulaziz University, Jeddah–21589, Saudi Arabia 5Department of Applied Mathematics, National Research Nuclear University, 31, Kashirskoe Hwy, Moscow–115409, Russian Federation 6Department of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Medunsa–0204, Pretoria, South Africa 7Radiation Physics Laboratory, Department of Physics, Faculty of Sciences, Badji Mokhtar University, P. O. Box 12, 23000 Annaba, Algeria 8Department of Mathematics, Faculty of Science and Arts, Yozgat Bozok University, 66100 Yozgat, Turkey} 9Institute of Physics Belgrade, Pregrevica, 118, 11080 Zemun, Serbia, e-mail: biswas.anjan@gmail.com Received 11 December 2020; in final form 17 February 2021; accepted 19 February 2021; published online 31 May 2021

This paper recovers a full spectrum of optical solitons that are generated by the combined effects of dispersion and nonlinearity of the pulse propagation. The quadratic-cubic form of the nonlinear refractive index is incorporated in the governing nonlinear Schrödinger equation, which governs the dynamics of the soliton transmission across trans-continental and transoceanic distances. The model is considered with a nonlinear chromatic dispersion that is required to sustain for smooth transmission of soliton pulses in optical fibers, couplers, PCF, magneto-optic waveguides, crystals, metamaterials, metasurfaces, birefringent fibers, DWDM systems and other form of waveguides. Solitons in birefringent fibers as well as solitons in polarization preserving fibers are considered. The governing model is treated with Hamiltonian type perturbation terms. The perturbation terms are with full intensity. The model is studied for the intensity count $m=1$. The adopted integration algorithm is the sine-Gordon equation method that reveals single form soliton solutions as well as dual-form soliton solutions. These solitons are dark soliton, singular soliton, bright soliton and combo singular soliton. Also, dark soliton represents a kink/anti-kink solitary wave or a shock wave in fluid dynamics. The respective constraint conditions are also in place to guarantee the existence of such solitons.

Key words: solitons, polarization, perturbation, quadratic–cubic nonlinearity

Full text

1. A. R. Adem et al., Phys. Lett. A 384, 126606 (2020);
   Crossref
2. M. Asma, W. A. M. Othman, B. R. Wong, A. Biswas, Proc. Roman. Acad. A 18, 331 (2017).
3. A. Biswas, M. Ekici, A. Sonmezoglu, M. Belic, Optik 178, 59 (2019);
   Crossref
4. A. Biswas, M. Ekici, A. Sonmezoglu, M. Belic, Optik 178, 117 (2019);
   Crossref
5. A. Biswas, M. Ekici, A. Sonmezoglu, M. Alfiras, Optik 178, 178 (2019);
   Crossref
6. A. Biswas et al., Chin. J. Phys. 56, 1990 (2018);
   Crossref
7. J. Fujioka et al., Chaos 21, 033120 (2011);
   Crossref
8. K. Hayata, M. Koshiba, J. Opt. Soc. Am. B 11, 2581 (1994);
   Crossref
9. S. Khan, Optik 212, 164706 (2020);
   Crossref
10. E. V. Krishnan et al., Chin. J. Phys. 60, 632 (2019);
    Crossref
11. N. A. Kudryashov, Optik 189, 42 (2019);
    Crossref
12. N. A. Kudryashov, E. V. Antonova, Optik 217, 164881 (2020);
    Crossref
13. N. A. Kudryashov, Optik 206, 163550 (2020);
    Crossref
14. N. A. Kudryashov, Chaos Solitons Fractals 141, 110325 (2020);
    Crossref
15. N. A. Kudryashov, Chaos Solitons Fractals 140, 110202 (2020);
    Crossref
16. N. A. Kudryashov, Chin. J. Phys. 66, 401 (2020);
    Crossref
17. H. Triki et al., Opt. Commun. 437, 392 (2019);
    Crossref
18. E. M. E. Zayed et al., Optik 202, 163620 (2020);
    Crossref
19. E. M. E. Zayed et al., Optik 203, 163993 (2020);
    Crossref
20. E. M. E. Zayed et al., Phys. Lett. A. 384, 126456 (2020);
    Crossref