Top

Optical and Quantum Electronics

Published in:

01-01-2024

Abundant optical soliton solutions to the Kudryashov equation and its modulation instability analysis

Author: Karmina K. Ali

Published in: Optical and Quantum Electronics | Issue 1/2024

Activate our intelligent search to find suitable subject content or patents.

search-config

AI-assisted search

Off

Abstract

This study investigate the Kudryashov equation, which is used to describe the propagation pulses in optical fibers. The aim of this study is to find closed-form wave solutions using the new modified generalized Riccati equation mapping method. By employing the proposed method, a range of new optical solutions with distinct shapes including dark, bright, combined dark-bright, singular periodic solutions are attained. These solutions are integrated with physical parameters and exhibit special waveform characteristics under specific constraints. The modulation instability analysis of the governing model is also presented. To illustrate the propagation of selected exact solutions, graphical representations in 2D, and 3D are provided with various parametric values. Additionally, the impact of the time parameter and the non-linearity degree n are also presented. It can be convincingly stated that the employed method is remarkably efficient and achieves significant success in discovering exact solutions for nonlinear partial differential equations.

previous article Application of wireless sensor network and Internet of things in building heating energy saving design

next article Propagation behavior of a generalized Hermite cosh-gaussian laser beam through marine environment

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

inform now

Abdel-Gawad, H.I., Sulaiman, T.A., Ismael, H.F.: Study of a nonlinear Schrodinger equation with truncated M proportional derivative. Optik 171252 (2023)

Agarwal, G.P.: Fiber Optic Communication Systems, 3rd edn. Wiley, Hoboken (2004)

Ali, K.K., Zabihi, A., Rezazadeh, H., Ansari, R., Inc, M.: Optical soliton with Kudryashov’s equation via sine-Gordon expansion and Kudryashov methods. Opt. Quant. Electron. 53, 1–15 (2021)

Ali, K.K., Yusuf, A., Ma, W.X.: Dynamical rational solutions and their interaction phenomena for an extended nonlinear equation. Commun. Theor. Phys. 75(3), 035001 (2023)MathSciNetADS

Allahyani, S.A., Rehman, H.U., Awan, A.U., Tag-ElDin, E.M., Hassan, M.U.: Diverse variety of exact solutions for nonlinear Gilson–Pickering equation. Symmetry 14(10), 2151 (2022)ADS

Arnous, A.H., Biswas, A., Ekici, M., Alzahrani, A.K., Belic, M.R.: Optical solitons and conservation laws of Kudryashov’s equation with improved modified extended tanh-function. Optik 225, 165406 (2021)ADS

Arnous, A.H., Zhou, Q., Biswas, A., Guggilla, P., Khan, S., Yıldırım, Y., Alshomrani, A.S., Alshehri, H.M.: Optical solitons in fiber Bragg gratings with cubic–quartic dispersive reflectivity by enhanced Kudryashov’s approach. Phys. Lett. A 422, 127797 (2022)MathSciNet

Atas, S.S., Ali, K.K., Sulaiman, T.A., Bulut, H.: Dynamic behavior of optical solitons to the coupled-Higgs equation through an efficient method. Int. J. Mod. Phys. B 37(15), 2350144 (2023)ADS

Biswas, A., Vega-Guzmán, J., Ekici, M., Zhou, Q., Triki, H., Alshomrani, A.S., Belic, M.R.: Optical solitons and conservation laws of Kudryashov’s equation using undetermined coefficients. Optik 202, 163417 (2020)ADS

Chen, Y.X., Xiao, X.: Vector soliton pairs for a coupled nonautonomous NLS model with partially nonlocal coupled nonlinearities under the external potentials. Nonlinear Dyn. 109(3), 2003–2012 (2022)

Eldidamony, H.A., Ahmed, H.M., Zaghrout, A.S., Ali, Y.S., Arnous, A.H.: Optical solitons with Kudryashov’s quintuple power law nonlinearity having nonlinear chromatic dispersion using modified extended direct algebraic method. Optik 262, 169235 (2022)ADS

Fang, Y., Wu, G.Z., Wang, Y.Y., Dai, C.Q.: Data-driven femtosecond optical soliton excitations and parameters discovery of the high-order NLSE using the PINN. Nonlinear Dyn. 105(1), 603–616 (2021)

Feng, B.F., Ling, L.: Darboux transformation and solitonic solution to the coupled complex short pulse equation. Physica D 437, 133332 (2022)MathSciNet

Geng, K.L., Zhu, B.W., Cao, Q.H., Dai, C.Q., & Wang, Y.Y.: Nondegenerate soliton dynamics of nonlocal nonlinear Schrödinger equation. Nonlinear Dyn. 1–14 (2023)

Guo, L., Chen, L., Mihalache, D., He, J.: Dynamics of soliton interaction solutions of the Davey–Stewartson I equation. Phys. Rev. E 105(1), 014218 (2022)MathSciNetPubMedADS

Hamid, I., Kumar, S.: Symbolic computation and Novel solitons, traveling waves and soliton-like solutions for the highly nonlinear (2+ 1)-dimensional Schrödinger equation in the anomalous dispersion regime via newly proposed modified approach. Opt. Quant. Electron. 55(9), 755 (2023)

Iqbal, I., Rehman, H.U., Mirzazadeh, M., Hashemi, M.S.: Retrieval of optical solitons for nonlinear models with Kudryashov’s quintuple power law and dual-form nonlocal nonlinearity. Opt. Quant. Electron. 55(7), 588 (2023)

Ismael, H.F., Ma, W.X., Bulut, H.: Dynamics of soliton and mixed lump-soliton waves to a generalized Bogoyavlensky–Konopelchenko equation. Phys. Scr. 96(3), 035225 (2021a)ADS

Ismael, H.F., Seadawy, A., Bulut, H.: Multiple soliton, fusion, breather, lump, mixed kink-lump and periodic solutions to the extended shallow water wave model in (2+1)-dimensions. Mod. Phys. Lett. B 35(08), 2150138 (2021b)MathSciNetADS

Kai, Y., Li, Y.: A study of Kudryashov equation and its chaotic behaviors. Waves Random Complex Media 1–17 (2023)

Kudryashov, N.A.: Traveling wave solutions of the generalized nonlinear Schrödinger equation with cubic-quintic nonlinearity. Optik 188, 27–35 (2019a)ADS

Kudryashov, N.A.: First integrals and general solution of the Fokas–Lenells equation. Optik 195, 163135 (2019b)ADS

Kudryashov, N.A.: A generalized model for description of propagation pulses in optical fiber. Optik 189, 42–52 (2019c)ADS

Kudryashov, N.A.: First integrals and general solution of the traveling wave reduction for Schrödinger equation with anti-cubic nonlinearity. Optik 185, 665–671 (2019d)ADS

Kudryashov, N.A.: First integrals and solutions of the traveling wave reduction for the Triki–Biswas equation. Optik 185, 275–281 (2019e)ADS

Kumar, S., Malik, S.: Cubic–quartic optical solitons with Kudryashov’s law of refractive index by Lie symmetry analysis. Optik 242, 167308 (2021)ADS

Kumar, S., Malik, S., Biswas, A., Zhou, Q., Moraru, L., Alzahrani, A.K., Belic, M.R.: Optical solitons with Kudryashov’s equation by Lie symmetry analysis. Phys. Wave Phenom. 28, 299–304 (2020)ADS

Li, B.Q., Ma, Y.L.: Interaction properties between rogue wave and breathers to the Manakov system arising from stationary self-focusing electromagnetic systems. Chaos Solitons Fractals 156, 111832 (2022)MathSciNet

Li, B.Q., Wazwaz, A.M., Ma, Y.L.: Two new types of nonlocal Boussinesq equations in water waves: bright and dark soliton solutions. Chin. J. Phys. 77, 1782–1788 (2022)MathSciNet

Luo, J., Fan, E.: \({\bar{\partial }}\)-dressing method for the coupled Gerdjikov–Ivanov equation. Appl. Math. Lett. 110, 106589 (2020)MathSciNet

Malik, S., Kumar, S.: Pure-cubic optical soliton perturbation with full nonlinearity by a new generalized approach. Optik 258, 168865 (2022)ADS

Malik, S., Kumar, S., Biswas, A., Yıldırım, Y., Moraru, L., Moldovanu, S., Iticescu, C., Alshehri, H.M.: Cubic-quartic optical solitons in fiber Bragg gratings with dispersive reflectivity having parabolic law of nonlinear refractive index by lie symmetry. Symmetry 14(11), 2370 (2022)ADS

Malik, S., Kumar, S., Biswas, A., Yıldırım, Y., Moraru, L., Moldovanu, S.P., Bibicu, D., Alotaibi, A.: Gap solitons in fiber Bragg gratings having polynomial law of nonlinear refractive index and cubic–quartic dispersive reflectivity by lie symmetry. Symmetry 15(5), 963 (2023a)ADS

Malik, S., Kumar, S., Nisar, K.S.: Invariant soliton solutions for the coupled nonlinear Schrödinger type equation. Alex. Eng. J. 66, 97–105 (2023b)

Murad, M.A.S.: New optical soliton solutions for time-fractional Kudryashov’s equation in optical fiber. Optik 283, 170897 (2023)ADS

Mynbaev, D.K., Gupta, S.C., Scheiner, L.L.: Fiber Optic Communications. Pearson Education, London (2005)

Prinari, B., Biondini, G., Trubatch, A.D.: Inverse scattering transform for the multi-component nonlinear Schrödinger equation with nonzero boundary conditions. Stud. Appl. Math. 126(3), 245–302 (2011)MathSciNet

Raheel, M., Inc, M., Tala-Tebue, E., Bayram, M.: Optical solitons of the Kudryashov equation via an analytical technique. Opt. Quant. Electron. 54(6), 340 (2022)

Rehman, H.U., Seadawy, A.R., Younis, M., Yasin, S., Raza, S.T., Althobaiti, S.: Monochromatic optical beam propagation of paraxial dynamical model in Kerr media. Results Phys. 31, 105015 (2021a)

Rehman, H.U., Ullah, N., Imran, M.A., Akgül, A.: Optical solitons of two non-linear models in birefringent fibres using extended direct algebraic method. Int. J. Appl. Comput. Math. 7(6), 227 (2021b)MathSciNet

Rehman, H.U., Seadawy, A.R., Razzaq, S., Rizvi, S.T.: Optical fiber application of the improved generalized Riccati equation mapping method to the perturbed nonlinear Chen–Lee–Liu dynamical equation. Optik 290, 171309 (2023)ADS

Shahzad, M.U., Rehman, H.U., Awan, A.U., Zafar, Z., Hassan, A.M., Iqbal, I.: Analysis of the exact solutions of nonlinear coupled Drinfeld–Sokolov–Wilson equation through \(\phi ^6\)-model expansion method. Results Phys. 52, 106771 (2023)

Sulaiman, T.A.: Three-component coupled nonlinear Schrödinger equation: optical soliton and modulation instability analysis. Phys. Scr. 95(6), 065201 (2020)ADS

Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: On dynamical behavior for optical solitons sustained by the perturbed Chen–Lee–Liu model. Commun. Theor. Phys. 74(7), 075005 (2022a)MathSciNetADS

Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: The dynamic behaviors of the Radhakrishnan–Kundu–Lakshmanan equation by Jacobi elliptic function expansion technique. Opt. Quant. Electron. 54(5), 292 (2022b)

Tarla, S., Ali, K.K., Yilmazer, R., Osman, M.S.: Applications of the generalized nonlinear evolution equation with symbolic computation approach. Mod. Phys. Lett. B 2350073 (2023)

Ullah, N., Asjad, M.I., Ur Rehman, H., Akgül, A.: Construction of optical solitons of Radhakrishnan–Kundu–Lakshmanan equation in birefringent fibers. Nonlinear Eng. 11(1), 80–91 (2022)ADS

Wang, R.R., Wang, Y.Y., Dai, C.Q.: Influence of higher-order nonlinear effects on optical solitons of the complex Swift–Hohenberg model in the mode-locked fiber laser. Opt. Laser Technol. 152, 108103 (2022)

Wen, X.K., Jiang, J.H., Liu, W., Dai, C.Q.: Abundant vector soliton prediction and model parameter discovery of the coupled mixed derivative nonlinear Schrödinger equation. Nonlinear Dyn. 1–13 (2023)

Yıldırım, Y.: Optical solitons to Sasa–Satsuma model with trial equation approach. Optik 184, 70–74 (2019a)ADS

Yildirim, Y.: Optical solitons of Biswas–Arshed equation by modified simple equation technique. Optik 182, 986–994 (2019b)ADS

Yıldırım, Y., Biswas, A., Asma, M., Ekici, M., Ntsime, B.P., Zayed, E.M., Moshokoa, S.P., Alzahrani, A.K., Belic, M.R.: Optical soliton perturbation with Chen–Lee–Liu equation. Optik 220, 165177 (2020)ADS

Yıldırım, Y., Topkara, E., Biswas, A., Triki, H., Ekici, M., Guggilla, P., Khan, S., Belic, M.R.: Cubic–quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by sine-Gordon equation approach. J. Opt. 50, 322–329 (2021)

Yin, Y.H., Lü, X., Ma, W.X.: Bäcklund transformation, exact solutions and diverse interaction phenomena to a (3+ 1)-dimensional nonlinear evolution equation. Nonlinear Dyn. 108(4), 4181–4194 (2022)

Yokus, A., Isah, M.A.: Dynamical behaviors of different wave structures to the Korteweg–de Vries equation with the Hirota bilinear technique. Physica A 622, 128819 (2023)MathSciNet

Younas, U., Ren, J.: Investigation of exact soliton solutions in magneto-optic waveguides and its stability analysis. Results Phys. 21, 103816 (2021)

Younas, U., Bilal, M., Ren, J.: Propagation of the pure-cubic optical solitons and stability analysis in the absence of chromatic dispersion. Opt. Quant. Electron. 53, 1–25 (2021)

Zayed, E.M., Alngar, M.E.: Optical soliton solutions for the generalized Kudryashov equation of propagation pulse in optical fiber with power nonlinearities by three integration algorithms. Math. Methods Appl. Sci. 44(1), 315–324 (2021)MathSciNetADS

Zayed, E.M., Gepreel, K.A., Shohib, R.M., Alngar, M.E., Yıldırım, Y.: Optical solitons for the perturbed Biswas–Milovic equation with Kudryashov’s law of refractive index by the unified auxiliary equation method. Optik 230, 166286 (2021)ADS

Zhou, Q., Triki, H., Xu, J., Zeng, Z., Liu, W., Biswas, A.: Perturbation of chirped localized waves in a dual-power law nonlinear medium. Chaos Solitons Fractals 160, 112198 (2022)MathSciNet

Title: Abundant optical soliton solutions to the Kudryashov equation and its modulation instability analysis
Author: Karmina K. Ali
Publication date: 01-01-2024
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 1/2024
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-023-05653-4

Springer Professional

Abstract

Please log in to get access to your license.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Other articles of this Issue 1/2024

Efficiency droop free UV-C LED by introducing p-doped LQB and p-n-p-n-p doped AlGaN hole injection layer

Retrieval of optical soliton solutions of stochastic perturbed Schrödinger-Hirota equation with Kerr law in the presence of spatio-temporal dispersion

Revised mathematical model for assessment of thermal characteristics developed in ultrafast pulse laser assisted nanoimprinting lithography on silicon based substrate surface

Leaky mode analysis using complex infinite elements

Blood component detection using photonic crystal fibre sensor

Comparison of 970- and 790-nm pumping for a 2.8 μm, Er3+-doped ZBLAN fiber laser