This paper addresses Radhakrishnan–Kundu–Lakshmanan equation that arises in the study of soliton dynamics in optical fibers. The bifurcation analysis is carried out and the phase portraits are displayed. The complete discriminant analysis also leads to solitons and other solutions to the model.
1. Radhakrishnan, R., Kundu, A. and Lakshmanan, M. Coupled nonlinear Schrödinger equations with cubic–quintic nonlinearity: integrability and soliton interaction in non-Kerr media. Phys. Rev. E, 1999, 60, 3314.
https://doi.org/10.1103/PhysRevE.60.3314
2. Garai, S. and Ghose-Choudhury, A. On the solution of the generalized Radhakrishnan–Kundu–Lakshmanan equation. Optik, 2021, 243, 167374.
https://doi.org/10.1016/j.ijleo.2021.167374
3. Huang, C. and Li, Z. Soliton solutions of conformable time-fractional perturbed Radhakrishnan–Kundu–Lakshmanan equation. AIMS Mathematics, 2022, 7(8), 14460–14473.
https://doi.org/10.3934/math.2022797
4. Kudryashov, N. A., Safonova, D. V. and Biswas, A. Painlevé analysis and a solution to the traveling wave reduction of the Radhakrishnan–Kundu–Lakshmanan Equation. Regul. Chaotic Dyn., 2019, 24, 607–614.
https://doi.org/10.1134/S1560354719060029
5. Kudryashov, N. A. The Radhakrishnan–Kundu–Lakshmanan equation with arbitrary refractive index and its exact solutions. Optik, 2021, 238, 166738.
https://doi.org/10.1016/j.ijleo.2021.166738
6. Kudryashov, N. A. Revised results of Khalida Bibi on the Radhakrishnan–Kundu–Lakshmanan equation. Optik, 2021, 240, 166898.
https://doi.org/10.1016/j.ijleo.2021.166898
7. Kudryashov, N. A. Solitary waves of the generalized Radhakrishnan–Kundu–Lakshmanan equation with four powers of non-linearity. Phys. Lett. A, 2022, 448, 128327.
https://doi.org/10.1016/j.physleta.2022.128327
8. Ozdemir, N. Optical solitons for Radhakrishnan–Kundu–Lakshmanan equation in the presence of perturbation term and having Kerr law. Optik, 2022, 271, 170127.
https://doi.org/10.1016/j.ijleo.2022.170127
9. Ozdemir, N., Esen, H., Secer, A., Bayram, M., Sulaiman, T. A., Yusuf, A. et al. Optical solitons and other solutions to the Radhakrishnan–Kundu–Lakshmanan equation. Optik, 2021, 242, 167363.
https://doi.org/10.1016/j.ijleo.2021.167363
10. Wang, K.-J. and Si, J. Optical solitons to the Radhakrishnan–Kundu–Lakshmanan equation by two effective approaches. Eur. Phys. J. Plus, 2022, 137, 1016.
https://doi.org/10.1140/epjp/s13360-022-03239-9
11. Biswas, A. Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by traveling wave hypothesis. Optik, 2018, 171, 217–220.
https://doi.org/10.1016/j.ijleo.2018.06.043
12. Bansal, A., Biswas, A., Mahmood, M. F., Zhou, Q., Mirzazadeh, M., Alshomrani, A. S. et al. Optical soliton perturbation with Radhakrishnan–Kundu–Lakshmanan equation by Lie group analysis. Optik, 2018, 163, 137–141.
https://doi.org/10.1016/j.ijleo.2018.02.104
13. Wazwaz, A.-M. Painlevé integrability and lump solutions for two extended (3 + 1)- and (2 + 1)-dimensional Kadomtsev–Petviashvili equations. Nonlinear Dyn., 2022, 111, 3623–3632.
https://doi.org/10.1007/s11071-022-08074-2
14. Wazwaz, A.-M., Hammad, M. A. and El-Tantawy, S. A. Bright and dark optical solitons for (3 + 1)-dimensional hyperbolic nonlinear Schrödinger equation using a variety of distinct schemes. Optik, 2022, 270, 170043.
https://doi.org/10.1016/j.ijleo.2022.170043
15. Li, J. and Dai, H. On the study of singular nonlinear traveling wave equations: dynamical system approach. Science Press, Beijing, 2007.
https://doi.org/10.1142/S0218127407019858
16. Li, J. B. Singular nonlinear traveling wave equations: bifurcation and exact solutions. Science Press, Beijing, 2013.
17. Yang, L., Hou, X. R., Zeng, Z. Complete discrimination system for polynomials. Sci. China Ser. E, 1996, 39(6), 628–646.
18. Tang, L. Bifurcation analysis and multiple solitons in birefringent fibers with coupled Schrödinger–Hirota equation. Chaos Fractals, 2022, 161, 112383.
https://doi.org/10.1016/j.chaos.2022.112383
19.Tang, L. Bifurcations and multiple optical solitons for the dual-modenonlinear Schrödinger equation with Kerr law nonlinearity. Optik, 2022, 265, 169555.
https://doi.org/10.1016/j.ijleo.2022.169555
20. Xie, Y., Yang, Z. and Li, L. New exact solutions to the high dispersive cubic–quintic nonlinear Schrödinger equation. Phys. Lett. A, 2018, 382(36), 2506–2514.
https://doi.org/10.1016/j.physleta.2018.06.023
21. Tang, L. Bifurcations and dispersive optical solitons for the nonlinear Schrödinger–Hirota equation in DWDM networks. Optik, 2022, 262, 169276.
https://doi.org/10.1016/j.ijleo.2022.169276
22. Tang, L. Bifurcations and disperive optical solitons for the cubic–quartic nonlinear Lakshmanan–Porsezian–Daniel equation in polarization-preserving fibers. Optik, 2022, 270, 170000.
https://doi.org/10.1016/j.ijleo.2022.170000
23. Tang, L. Bifurcations and optical solitons for the coupled nonlinear Schrödinger equation in optical fiber Bragg gratings. J. Opt., 2022, 52, 581–592.
https://doi.org/10.1007/s12596-022-00963-4
24. Zhou, J., Zhou, R. and Zhu, S. Peakon, rational function and periodic solutions for Tzitzeica–Dodd–Bullough type equations. Chaos Solitons Fractals, 2020, 141, 110419.
https://doi.org/10.1016/j.chaos.2020.110419
25. Xie, Y., Li, L. and Kang, Y. New solitons and conditional stability to the high dispersive nonlinear Schrödinger equation with parabolic law nonlinearity. Nonlinear Dyn., 2021, 103, 1011–1021.
https://doi.org/10.1007/s11071-020-06141-0
