Abstract
The major goal of the present paper is to construct optical solitons of the Ginzburg–Landau equation including the parabolic nonlinearity. Such an ultimate goal is formally achieved with the aid of symbolic computation, a complex transformation, and Kudryashov and exponential methods. Several numerical simulations are given to explore the influence of the coefficients of nonlinear terms on the dynamical features of the obtained optical solitons. To the best of the authors’ knowledge, the results reported in the current study, classified as bright and kink solitons, have a significant role in completing studies on the Ginzburg–Landau equation including the parabolic nonlinearity.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Akbar, M.A., Akinyemi, L., Yao, S.W., Jhangeer, A., Rezazadeh, H., Khater, M.M.A., Ahmad, H., Inc, M.: Soliton solutions to the Boussinesq equation through sine-Gordon method and Kudryashov method. Results Phys. 25, 104228 (2021)
Akinyemi, L.: Two improved techniques for the perturbed nonlinear Biswas–Milovic equation and its optical solitons. Optik 243, 167477 (2021)
Akinyemi, L., Rezazadeh, H., Shi, Q.H., Inc, M., Khater, M.M.A., Ahmad, H., Jhangeer, A., Ali Akbar, M.: New optical solitons of perturbed nonlinear Schrödinger–Hirota equation with spatio-temporal dispersion. Results Phys. 29, 104656 (2021a)
Akinyemi, L., Hosseini, K., Salahshour, S.: The bright and singular solitons of (2+1)-dimensional nonlinear Schrödinger equation with spatio-temporal dispersions. Optik 242, 167120 (2021b)
Ali, A.T., Hassan, E.R.: General expa function method for nonlinear evolution equations. Appl. Math. Comput. 217, 451–459 (2010)
Arshed, S., Biswas, A., Mallawi, F., Belic, M.R.: Optical solitons with complex Ginzburg–Landau equation having three nonlinear forms. Phys. Lett. A 383, 126026 (2019)
Bekir, A.: Application of the (G/G)-expansion method for nonlinear evolution equations. Phys. Lett. A 372, 3400–3406 (2008)
Bekir, A., Shehata, M.S.M., Zahran, E.H.M.: New optical soliton solutions for the thin-film ferroelectric materials equation instead of the numerical solution. Comput. Methods Differ. Equ. 10, 158–167 (2021). https://doi.org/10.22034/cmde.2020.38121.1677
Biswas, A.: Chirp-free bright optical solitons and conservation laws for complex Ginzburg–Landau equation with three nonlinear forms. Optik 174, 207–215 (2018)
Elboree, M.K.: Optical solitons for complex Ginzburg–Landau model with Kerr, quadratic-cubic and parabolic law nonlinearities in nonlinear optics by the exp(-ϕ(ξ) expansion method. Pramana J. Phys. 94, 139 (2020)
He, J.H., Wu, X.H.: Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30, 700–708 (2006)
Hosseini, K., Mirzazadeh, M., Rabiei, F., Baskonus, H.M., Yel, G.: Dark optical solitons to the Biswas–Arshed equation with high order dispersions and absence of self-phase modulation. Optik 209, 164576 (2020a)
Hosseini, K., Mirzazadeh, M., Osman, M.S., Al Qurashi, M., Baleanu, D.: Solitons and Jacobi elliptic function solutions to the complex Ginzburg–Landau equation. Front. Phys. 8, 225 (2020b)
Hosseini, K., Salahshour, S., Mirzazadeh, M.: Bright and dark solitons of a weakly nonlocal Schrödinger equation involving the parabolic law nonlinearity. Optik 227, 166042 (2021a)
Hosseini, K., Mirzazadeh, M., Baleanu, D., Raza, N., Park, C., Ahmadian, A., Salahshour, S.: The generalized complex Ginzburg–Landau model and its dark and bright soliton solutions. Eur. Phys. J. Plus 136, 709 (2021b)
Inc, M., Ates, E., Tchier, F.: Optical solitons of the coupled nonlinear Schrödinger’s equation with spatiotemporal dispersion. Nonlinear Dyn. 85, 1319–1329 (2016)
Kilic, B., Inc, M.: On optical solitons of the resonant Schrödinger’s equation in optical fibers with dual-power law nonlinearity and time-dependent coefficients. Waves Random Complex Media 25, 334–341 (2015)
Kilic, B., Inc, M.: Optical solitons for the Schrödinger–Hirota equation with power law nonlinearity by the Bäcklund transformation. Optik 138, 64–67 (2017)
Kudryashov, N.A.: Method for finding highly dispersive optical solitons of nonlinear differential equation. Optik 206, 163550 (2020a)
Kudryashov, N.A.: Highly dispersive solitary wave solutions of perturbed nonlinear Schrödinger equations. Appl. Math. Comput. 371, 124972 (2020b)
Kudryashov, N.A.: Highly dispersive optical solitons of the generalized nonlinear eighth-order Schrödinger equation. Optik 206, 164335 (2020c)
Mirzazadeh, M., Ekici, M., Sonmezoglu, A., Eslami, M., Zhou, Q., Kara, A.H., Milovic, D., Majid, F.B., Biswas, A., Belic, M.: Optical solitons with complex Ginzburg–Landau equation. Nonlinear Dyn. 85, 1979–2016 (2016)
Nisar, K.S., Ciancio, A., Ali, K.K., Osman, M.S., Cattani, C., Baleanu, D., Zafar, A., Raheel, M., Azeem, M.: On beta-time fractional biological population model with abundant solitary wave structures. Alex. Eng. J. 61, 1996–2008 (2021). https://doi.org/10.1016/j.aej.2021.06.106
Osman, M.S., Ghanbari, B., Machado, J.A.T.: New complex waves in nonlinear optics based on the complex Ginzburg–Landau equation with Kerr law nonlinearity. Eur. Phys. J. Plus 134, 20 (2019)
Ouahid, L., Abdou, M.A., Owyed, S., Inc, M., Abdel-Baset, A.M., Yusuf, A.: New optical solitons for complex Ginzburg–Landau equation with beta derivatives via two integration algorithms. Indian J. Phys. 96, 2093–2105 (2021). https://doi.org/10.1007/s12648-021-02168-0
Rezazadeh, H.: New solitons solutions of the complex Ginzburg–Landau equation with Kerr law nonlinearity. Optik 167, 218–227 (2018)
Rezazadeh, H., Inc, M., Baleanu, D.: New solitary wave solutions for variants of (3+1)-dimensional Wazwaz–Benjamin–Bona–Mahony equations. Front. Phys. 8, 332 (2020a)
Rezazadeh, H., Abazari, R., Khater, M.M.A., Inc, M., Baleanu, D.: New optical solitons of conformable resonant nonlinear Schrödinger’s equation. Open Phys. 18, 761–769 (2020b)
Siddique, I., Jaradat, M.M.M., Zafar, A., Mehdi, K.B., Osman, M.S.: Exact traveling wave solutions for two prolific conformable M-fractional differential equations via three diverse approaches. Results Phys. 28, 104557 (2021)
Sulaiman, T.A., Baskonus, H.M., Bulut, H.: Optical solitons and other solutions to the conformable space-time fractional complex Ginzburg–Landau equation under Kerr law nonlinearity. Pramana J. Phys. 91, 58 (2018)
Tchier, F., Aslan, E.C., Inc, M.: Optical solitons in parabolic law medium: Jacobi elliptic function solution. Nonlinear Dyn. 85, 2577–2582 (2016)
Tchier, F., Inc, M., Kilic, B., Akgül, A.: On soliton structures of generalized resonance equation with time dependent coefficients. Optik 128, 218–223 (2017)
Wang, M., Li, X., Zhang, J.: The (G/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372, 417–423 (2008)
Yan, C.: A simple transformation for nonlinear waves. Phys. Lett. A 224, 77–84 (1996)
Yıldırım, Y., Biswas, A., Khan, S., Guggilla, P., Alzahrani, A.K., Belic, M.R.: Optical solitons in fiber Bragg gratings with dispersive reflectivity by sine-Gordon equation approach. Optik 237, 166684 (2021a)
Yıldırım, Y., Biswas, A., Dakova, A., Khan, S., Moshokoa, S.P., Alzahrani, A.K., Belic, M.R.: Cubic-quartic optical soliton perturbation with Fokas–Lenells equation by sine-Gordon equation approach. Results Phys. 26, 104409 (2021b)
Funding
The authors have not disclosed any funding.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
Conflict of interest
The authors declare no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Hosseini, K., Mirzazadeh, M., Akinyemi, L. et al. Optical solitons to the Ginzburg–Landau equation including the parabolic nonlinearity. Opt Quant Electron 54, 631 (2022). https://doi.org/10.1007/s11082-022-03884-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-022-03884-5