Optical soliton and travelling wave solutions for the wick-type stochastic Fokas-Lenells equation
DOI:
https://doi.org/10.31349/RevMexFis.71.041302Keywords:
Optical solitons, travelling wave solutions, Fokas-Lenells equation, Wick product, Hermite transformAbstract
In this study, we investigate the perturbed Fokas-Lenells equation with conformable fractional derivatives in the presence of white noise, employing two advanced methodologies. The analysis utilizes Hermite and inverse Hermite transformations within the framework of white noise theory to derive solutions to the model. We also construct traveling wave solutions, optical soliton solutions, and their respective stochastic counterparts.
References
He, J., Xu, S., Porsezian, K.: Rogue waves of the Fokas–Lenells equation. J. Phys. Soc. Jpn.(2012).
https://doi.org/10.1143/JPSJ.81.124007
Du, Z., Meng, G.Q., Du, X.X.: Localized waves and breather-to-soliton conversions of the coupled Fokas–Lenells system. Chaos,
Solitons & Fract. (2021). https://doi.org/10.1016/j.chaos.2021.111507
Triki, H., Wazwaz, A.M.: Combined optical solitary waves of the Fokas-Lenells equation. Waves Random Complex Medium (2017).
https://doi.org/10.1080/17455030.2017.1285449
Liu, F., Zhou,C.C., Lü, X., Xu, H.: Dynamic behaviors of optical solitons for Fokas-Lenells equation in optical fiber. Optik (2020).
https://doi.org/10.1016/j.ijleo.2020.165237
Yıldırım, Y., Biswas, A., Dakova, A., Khan, S., Moshokoa, S.P., Alzahrani, A.K., Belici, M.R.: Cubic–quartic
optical soliton perturbation with Fokas–Lenells equation by sine–Gordon equation approach. Results in Phys. (2021)
https://doi.org/10.1016/j.rinp.2021.104409
Holden, H., Øksendal, B., Ubøe, J., Zhang, T.: Stochastic partial differential equations: A Modeling, White Noise Functional Approach.
Birkhäuser, Basel (1996)
Baronio, F., Chen, S., Grelu, Ph., Wabnitz, S., Conforti, M.: Baseband modulation instability as the origin of rogue waves. Phys. Rev.
A. (2015). https://doi.org/10.1103/PhysRevA.91.033804
Chen, S. Ye, Y., Soto-Crespo, J.M., Grelu, Ph., Baroni, F.: Peregrine solitons beyond the threefold limit and their two-soliton interactions.
Phys. Rev. Lett. (2018). https://doi.org/10.1103/PhysRevLett.121.104101
Han, H.B., Li, H.J., Dai, C.Q.: Wick-type stochastic multi-soliton and soliton molecule solutions in the framework of nonlinear
Schrödinger equation. Appl. Math. Lett. (2021). https://doi.org/10.1016/j.aml.2021.107302
Chen, B., Xie, Y.: Periodic-like solutions of variable coefficient and Wick-type stochastic NLS equations. J. Comput. Appl. Math.
(2007). https://doi.org/10.1016/j.cam.2006.04.002
Yulin, Y. L., Yao, Z. Z.: Stochastic exact solutions of the Wick-type stochastic NLS equation. Appl. Math. and Comput. (2014).
https://doi.org/10.1016/j.amc.2014.09.083
Olivera, C., Tudor, C.A.: Absolute continuity of the solution to the stochastic Burgers equation. Chaos Solitons & Fractals (2021).
https://doi.org/10.1016/j.chaos.2021.111635
Xiao, G.,Wang, J.R., O’Regan, D.: Existence, uniqueness and continuous dependence of solutions to conformable stochastic differential
equations. Chaos, Solitons & Fract. (2020). https://doi.org/10.1016/j.chaos.2020.110269
Kim, H.,Sakthivel, R., Debbouche, A., Torres, D.F.M.: Traveling wave solutions of some important Wick-type fractional stochastic
nonlinear partial differential equations. Chaos, Solitons & Fract. (2020). https://doi.org/10.1016/j.chaos.2019.109542
He, T., Wang, Y.Y.: Dark-multi-soliton and soliton molecule solutions of stochastic nonlinear Schrödinger equation in the white noise
space. Appl. Math. Lett. (2021). https://doi.org/10.1016/j.aml.2021.107405
Ulutas E.: Traveling wave and optical soliton solutions of theWick-type stochastic NLSE with conformable derivatives, Chaos, Solitons
& Fract. (2021). https://doi.org/10.1016/j.chaos.2021.111052
Choi, J.H., Kim, H.: The Wick-type explicit solutions of the nonlinear stochastic Wick-type fractional Gardner equation. Results in
Phys.(2021). https://doi.org/10.1016/j.rinp.2021.104886
Khalil, R., Horani, M.A., Yousef, A., Sababheh, M.: A new definition of fractional derivative. J Comput Appl Math. (2014).
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2025 Esma Ulutaş

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Authors retain copyright and grant the Revista Mexicana de Física right of first publication with the work simultaneously licensed under a CC BY-NC-ND 4.0 that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.