In the present investigation, we employed the Jacobi elliptic function (JEF) method to invoke the perturbed nonlinear Schrödinger equation with self-steepening (SS), self-phase modulation (SPM), and group velocity dispersion (GVD), which govern the propagation of solitonic pulses in optical fibres. The proposed algorithm proves the existence of the family of solitons in optical fibers. Consequently, chirped and chirp free W-shaped bright, dark soliton solutions are obtained from dn(ξ), cn(ξ) and sn(ξ) functions. The final results are displayed in three-dimensional plots with specific physical values of GVD, SPM and SS for an optical fiber.
1. Mollenauer, L. F., Stolen, R. H. and Gordon, J. P. Experimental observation of picosecond pulse narrowing and solitons in optical fibers. Phys. Rev. Lett., 1980, 45, 1095.
https://doi.org/10.1103/PhysRevLett.45.1095
2. Malomed, B. A. Ideal amplification of an ultrashort soliton in a dispersion-decreasing fiber. Opt. Lett., 1994, 19, 341.
https://doi.org/10.1364/OL.19.000341
3. Liu, W. Parallel line rogue waves of a (2+1)-dimensional nonlinear Schrödinger equation describing the Heisenberg ferromagnetic spin chain. Romanian J. Phys., 2017, 62, 1–16.
4. Muniyappan, A., Sharon L. N. and Suruthi, A. Excitations of periodic kink breathers and dark/bright breathers in a microtubulin protofilament lattices. Nonlinear Dyn., 2021, 106, 3495–3506.
https://doi.org/10.1007/s11071-021-06979-y
5. Wazwaz, A. M. A sine-cosine method for handling nonlinear wave equations. Math. Comput. Model., 2004, 40, 499–508.
https://doi.org/10.1016/j.mcm.2003.12.010
6. Akram, G., Arshed, S. and Imran, Z. Soliton solutions for fractional DNA Peyrard–Bishop equation via the extended (G′/G2)-expansion method. Physica Scr., 2021, 96, 094009.
https://doi.org/10.1088/1402-4896/ac0955
7. Biswas, A., Jawad, A. J. M., Manrakhan, W. N., Sarma, A. K. and Khan, K. R. Optical solitons and complexitons of the Schrödinger–Hirota equation. Opt. Laser Technol., 2012, 44(7), 2265–2269.
https://doi.org/10.1016/j.optlastec.2012.02.028
8. Rezazadeh, H., Ullah, N., Akinyemi, L., Shah, A., Mirhosseini-Alizamin, S. M., Chu, Y. M. and Ahmad, H. Optical soliton solutions of the generalized non-autonomous nonlinear Schrödinger equations by the new Kudryashov’s method. Results Phys., 2021, 24, 104179.
https://doi.org/10.1016/j.rinp.2021.104179
9. Akinyemi, L., Senol, M., Mirzazadeh, M. and Eslami, M. Optical solitons for weakly nonlocal Schrödinger equation with parabolic law nonlinearity and external potential. Optik, 2021, 230, 166281.
https://doi.org/10.1016/j.ijleo.2021.166281
10. Radha, R. and Lakshmanan, M. Singularity structure analysis and bilinear form of a (2 + 1) dimensional non-linear Schrödinger (NLS) equation. Inverse Problems, 1994, 10, 29–32.
https://doi.org/10.1088/0266-5611/10/4/002
11. Biswas, A., Rezazadeh, H., Mirzazadeh, M., Eslami, M., Zhou, Q., Moshokoa, S. P. and Belic, M. Optical solitons having weak non-local nonlinearity by two integration schemes. Optik, 2018, 164, 380–384.
https://doi.org/10.1016/j.ijleo.2018.03.026
12. Zhou, Q., Liu, L., Zhang, H., Mirzazadeh, M., Bhrawy, A. H., Zerrad, E. et al. Dark and singular optical solitons with competing nonlocal nonlinearities. Opt. Appl., 2016, 46, 79–86.
13. Wazwaz, A. M. Multiple-soliton solutions of two extended model equations for shallow water waves. Appl. Math. Comput., 2008, 201, 790–799.
https://doi.org/10.1016/j.amc.2008.01.017
14. Sakaguchi, H. and Malomed, B. A. Gross–Pitaevskii–Poisson model for an ultracold plasma: Density waves and solitons. Phys. Rev. Research, 2020, 2, 033188.
https://doi.org/10.1103/PhysRevResearch.2.033188
15. Muniyappan, A., Sahasraari, L. N., Anitha, S., Ilakiya, S., Biswas, A., Yıldırım, Y. et al. Family of optical solitons for perturbed Fokas–Lenells equation. Optik, 2022, 249, 168224.
https://doi.org/10.1016/j.ijleo.2021.168224
16. Biswas, A. and Milovic, D. Bright and dark solitons of the generalized nonlinear Schrödinger’s equation. Commun. Nonlinear Sci. Numer. Simul., 2010, 15, 1473–1484.
https://doi.org/10.1016/j.cnsns.2009.06.017
17. Muniyappan, A., Monisha, P., Priya, E. K. and Nivetha, V. Generation of wing-shaped dark soliton for perturbed Gerdjikov–Ivanov equation in optical fibre. Optik, 2021, 230, 166328.
https://doi.org/10.1016/j.ijleo.2021.166328
18. Kivshar, Y. S. and Agrawal, G. P. Optical Solitons: From Fibers to Photonic Crystals. Academic Press, San Diego, California, 2003.
https://doi.org/10.1016/B978-012410590-4/50012-7
19. Goyal, A., Gupta, R., Kumar, C. N. and Raju, T. S. Chirped femtosecond solitons and double-kink solitons in the cubic-quintic nonlinear Schrödinger equation with self-steepening and self-frequency shift. Phys. Rev. A, 2011, 84, 063830.
https://doi.org/10.1103/PhysRevA.84.063830
20. Vyas, V. M., Patel, P., Panigrahi, P. K., Kumar, C. N. and Greiner, W. Chirped chiral solitons in the nonlinear Schrödinger equation with self-steepening and self-frequency shift. Phys. Rev. A, 2008, 78, 021803(R).
https://doi.org/10.1103/PhysRevA.78.021803
21. Kumar, C. N. and Durganandini, P. New phase modulated solutions for a higher-order nonlinear Schrödinger equation. Pramana J. Phys., 1999, 53, 271.
22. Triki, H., Biswas, A., Milovic, D. and Belic, M. Chirped femtosecond pulses in the higher-order nonlinear Schrödinger equation with non-Kerr nonlinear terms and cubic-quintic-septic nonlinearities. Opt. Commun., 2016, 366, 362–369.
https://doi.org/10.1016/j.optcom.2016.01.005
23. Triki, H., Porsezian, K. and Grelu, P. Chirped soliton solutions for the generalized nonlinear Schrödinger equation with polynomial nonlinearity and non-Kerr terms of arbitrary order. J. Opt., 2016, 18, 075504.
https://doi.org/10.1088/2040-8978/18/7/075504
24. Triki, H., Porsezian, K., Choudhuri, A. and Dinda, P. T. Chirped solitary pulses for a nonic nonlinear Schrödinger equation on a continuous-wave background. Phys. Rev. A, 2016, 93, 063810.
https://doi.org/10.1103/PhysRevA.93.063810
25. Desaix, M., Helczynski, L., Anderson, D. and Lisak, M. Propagation properties of chirped soliton pulses in optical nonlinear Kerr media. Phys. Rev. E, 2002, 65, 056602.
https://doi.org/10.1103/PhysRevE.65.056602
