Skip to main content
Erschienen in: Optical and Quantum Electronics 5/2022

01.05.2022

Optical solitons in metamaterials with third and fourth order dispersions

verfasst von: Thilagarajah Mathanaranjan, Dipankar Kumar, Hadi Rezazadeh, Lanre Akinyemi

Erschienen in: Optical and Quantum Electronics | Ausgabe 5/2022

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The propagation of optical solitons via nonlinear metamaterials with cubic-quintic nonlinearity, detuning intermodal dispersion, self steepening effect, and nonlinear third and fourth-order dispersions is the focus of this study. To find the optical solitons and other solutions, the extended sinh-Gordon equation expansion method is applied to the aforementioned model. As a result, dark, bright, combined dark–bright, singular, combined singular soliton, and singular periodic wave solutions are obtained. To our best knowledge, the application of the method to the model, and the acquired combined soliton solutions are novel. To understand the nonlinear propagation theory of solitons in metamaterials, the reported outcomes can be enriched by the soliton theory.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

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!

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!

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!

Literatur
Zurück zum Zitat Akinyemi, L., Şenol, M., Akpan, U., Oluwasegun, K.: The optical soliton solutions of generalized coupled nonlinear Schrödinger-Korteweg-de Vries equations. Opt. Quant. Electron. 53(7), 1–14 (2021)CrossRef Akinyemi, L., Şenol, M., Akpan, U., Oluwasegun, K.: The optical soliton solutions of generalized coupled nonlinear Schrödinger-Korteweg-de Vries equations. Opt. Quant. Electron. 53(7), 1–14 (2021)CrossRef
Zurück zum Zitat Akinyemi, L., Inc, M., Khater, M.M.A., Rezazadehn, H.: Dynamical behaviour of Chiral nonlinear Schrödinger equation. Opt. Quant. Electron. 54, 191 (2022b) Akinyemi, L., Inc, M., Khater, M.M.A., Rezazadehn, H.: Dynamical behaviour of Chiral nonlinear Schrödinger equation. Opt. Quant. Electron. 54, 191 (2022b)
Zurück zum Zitat Attia, R.A., Lu, D., Ak, T., Khater, M.M.: Optical wave solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term via modified Khater method. Mod. Phys. Lett. B 34(05), 2050044 (2020)ADSCrossRef Attia, R.A., Lu, D., Ak, T., Khater, M.M.: Optical wave solutions of the higher-order nonlinear Schrödinger equation with the non-Kerr nonlinear term via modified Khater method. Mod. Phys. Lett. B 34(05), 2050044 (2020)ADSCrossRef
Zurück zum Zitat Biswas, A., Milovic, M., Edwards, M.: Mathematical Theory of Dispersion-Managed Optical Solitons. Springer, New York (2010)MATHCrossRef Biswas, A., Milovic, M., Edwards, M.: Mathematical Theory of Dispersion-Managed Optical Solitons. Springer, New York (2010)MATHCrossRef
Zurück zum Zitat Biswas, A., Khan, K.R., Mahmood, M.F., Belic, M.: Bright and dark solitons in optical metamaterials. Optik 125(13), 3299–3302 (2014)ADSCrossRef Biswas, A., Khan, K.R., Mahmood, M.F., Belic, M.: Bright and dark solitons in optical metamaterials. Optik 125(13), 3299–3302 (2014)ADSCrossRef
Zurück zum Zitat Cai, W., Shalaev, V.: Optical Metamaterials: Fundamentals and Application. Springer, New York (2010)CrossRef Cai, W., Shalaev, V.: Optical Metamaterials: Fundamentals and Application. Springer, New York (2010)CrossRef
Zurück zum Zitat Cimpoiasu, R., Pauna, A.S.: Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method. Open Phys. 16(1), 419–426 (2018)CrossRef Cimpoiasu, R., Pauna, A.S.: Complementary wave solutions for the long-short wave resonance model via the extended trial equation method and the generalized Kudryashov method. Open Phys. 16(1), 419–426 (2018)CrossRef
Zurück zum Zitat Ghanbari, B.: On novel non differentiable exact solutions to local fractional Gardner’s equation using an effective technique. Math. Methods Appl. Sci. 44(6), 4673–4685 (2021a)MATHCrossRef Ghanbari, B.: On novel non differentiable exact solutions to local fractional Gardner’s equation using an effective technique. Math. Methods Appl. Sci. 44(6), 4673–4685 (2021a)MATHCrossRef
Zurück zum Zitat Ghanbari, B.: Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative. Math. Methods Appl. Sci. 44(11), 8759–8774 (2021b) Ghanbari, B.: Abundant exact solutions to a generalized nonlinear Schrödinger equation with local fractional derivative. Math. Methods Appl. Sci. 44(11), 8759–8774 (2021b)
Zurück zum Zitat Ghanbari, B., Nisar, K.S., Aldhaifallah, M.: Abundant solitary wave solutions to an extended nonlinear Schrödinger equation with conformable derivative using an efficient integration method. Adv. Differ. Equ. 2020(1), 1–25 (2020)MATHCrossRef Ghanbari, B., Nisar, K.S., Aldhaifallah, M.: Abundant solitary wave solutions to an extended nonlinear Schrödinger equation with conformable derivative using an efficient integration method. Adv. Differ. Equ. 2020(1), 1–25 (2020)MATHCrossRef
Zurück zum Zitat Hashemi, M.S., Inc, M., Bayram, M.: Symmetry properties and exact solutions of the time fractional Kolmogorov–Petrovskii–Piskunov equation. Revista mexicana de fisica 65(5), 529–535 (2019)MathSciNetCrossRef Hashemi, M.S., Inc, M., Bayram, M.: Symmetry properties and exact solutions of the time fractional Kolmogorov–Petrovskii–Piskunov equation. Revista mexicana de fisica 65(5), 529–535 (2019)MathSciNetCrossRef
Zurück zum Zitat Hosseini, K., Kaur, L., Mirzazadeh, M., Baskonus, H.M.: 1-Soliton solutions of the \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative. Opt. Quant. Electron. 53(2), 1–10 (2021a) Hosseini, K., Kaur, L., Mirzazadeh, M., Baskonus, H.M.: 1-Soliton solutions of the \((2+1)\)-dimensional Heisenberg ferromagnetic spin chain model with the beta time derivative. Opt. Quant. Electron. 53(2), 1–10 (2021a)
Zurück zum Zitat Hubert, M.B., Nestor, S., Betchewe, G., Biswas, A., Khan, S., Doka, S.Y., Zhou, Q., Ekici, M., Belic, M.: Dispersive solitons in optical metamaterials having parabolic form of nonlinearity. Optik 179, 1009–1018 (2019)ADSCrossRef Hubert, M.B., Nestor, S., Betchewe, G., Biswas, A., Khan, S., Doka, S.Y., Zhou, Q., Ekici, M., Belic, M.: Dispersive solitons in optical metamaterials having parabolic form of nonlinearity. Optik 179, 1009–1018 (2019)ADSCrossRef
Zurück zum Zitat Kader, A.A., Latif, M.A., Zhou, Q.: Exact optical solitons in metamaterials with anti-cubic law of nonlinearity by Lie group method. Opt. Quant. Electron. 51(1), 1–8 (2019)CrossRef Kader, A.A., Latif, M.A., Zhou, Q.: Exact optical solitons in metamaterials with anti-cubic law of nonlinearity by Lie group method. Opt. Quant. Electron. 51(1), 1–8 (2019)CrossRef
Zurück zum Zitat Khater, M., Jhangeer, A., Rezazadeh, H., Akinyemi, L., Akbar, M.A., Inc, M., Ahmad, H.: New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques. Opt. Quant. Electron. 53(11), 1–27 (2021)CrossRef Khater, M., Jhangeer, A., Rezazadeh, H., Akinyemi, L., Akbar, M.A., Inc, M., Ahmad, H.: New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques. Opt. Quant. Electron. 53(11), 1–27 (2021)CrossRef
Zurück zum Zitat Korpinar, Z., Inc, M., Bayram, M., Hashemi, M.S.: New optical solitons for Biswas–Arshed equation with higher order dispersions and full nonlinearity. Optik 206, 163332 (2020)ADSCrossRef Korpinar, Z., Inc, M., Bayram, M., Hashemi, M.S.: New optical solitons for Biswas–Arshed equation with higher order dispersions and full nonlinearity. Optik 206, 163332 (2020)ADSCrossRef
Zurück zum Zitat Kumar, D., Manafian, J., Hawlader, F., Ranjbaran, A.: New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method. Optik 160, 159–167 (2018)ADSCrossRef Kumar, D., Manafian, J., Hawlader, F., Ranjbaran, A.: New closed form soliton and other solutions of the Kundu–Eckhaus equation via the extended sinh-Gordon equation expansion method. Optik 160, 159–167 (2018)ADSCrossRef
Zurück zum Zitat Kumar, D., Joardar, A.K., Hoque, A., Paul, G.C.: Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method. Opt. Quant. Electron. 51(7), 1–36 (2019)CrossRef Kumar, D., Joardar, A.K., Hoque, A., Paul, G.C.: Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method. Opt. Quant. Electron. 51(7), 1–36 (2019)CrossRef
Zurück zum Zitat Kumar, D., Paul, G.C.: Solitary and periodic wave solutions to the family of nonlinear conformable fractional Boussinesq-like equations. Math. Methods Appl. Sci. 44(4), 3138–3158 (2021)ADSMathSciNetMATHCrossRef Kumar, D., Paul, G.C.: Solitary and periodic wave solutions to the family of nonlinear conformable fractional Boussinesq-like equations. Math. Methods Appl. Sci. 44(4), 3138–3158 (2021)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Mathanaranjan, T.: Solitary wave solutions of the Camassa–Holm-nonlinear Schrödinger equation. Res. Phys. 19, 103549 (2020) Mathanaranjan, T.: Solitary wave solutions of the Camassa–Holm-nonlinear Schrödinger equation. Res. Phys. 19, 103549 (2020)
Zurück zum Zitat Mathanaranjan, T.: Soliton solutions of deformed nonlinear Schrödinger equations using ansatz method. Int. J. Appl. Comput. Math. 7, 159 (2021a) Mathanaranjan, T.: Soliton solutions of deformed nonlinear Schrödinger equations using ansatz method. Int. J. Appl. Comput. Math. 7, 159 (2021a)
Zurück zum Zitat Mathanaranjan, T.: Exact and explicit traveling wave solutions to the generalized Gardner and BBMB equations with dual high-order nonlinear terms. Partial Differ. Equ. Appl. Math. 4, 100120 (2021b) Mathanaranjan, T.: Exact and explicit traveling wave solutions to the generalized Gardner and BBMB equations with dual high-order nonlinear terms. Partial Differ. Equ. Appl. Math. 4, 100120 (2021b)
Zurück zum Zitat Nuruzzaman, M., Kumar, D., Paul, G.C.: Fractional low-pass electrical transmission line model: dynamic behaviors of exact solutions with the impact of fractionality and free parameters. Res. Phys. 27, 104457 (2021) Nuruzzaman, M., Kumar, D., Paul, G.C.: Fractional low-pass electrical transmission line model: dynamic behaviors of exact solutions with the impact of fractionality and free parameters. Res. Phys. 27, 104457 (2021)
Zurück zum Zitat Seadawy, A.R., Kumar, D., Chakrabarty, A.K.: Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method. Eur. Phys. J. Plus 133(5), 1–11 (2018)CrossRef Seadawy, A.R., Kumar, D., Chakrabarty, A.K.: Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method. Eur. Phys. J. Plus 133(5), 1–11 (2018)CrossRef
Zurück zum Zitat Xie, F.D., Li, M., Zhang, Y.: Exact solutions of some systems of nonlinear partial differential equations using symbolic computation. Comput. Math. Appl. 44(6), 711–716 (2002)MathSciNetMATHCrossRef Xie, F.D., Li, M., Zhang, Y.: Exact solutions of some systems of nonlinear partial differential equations using symbolic computation. Comput. Math. Appl. 44(6), 711–716 (2002)MathSciNetMATHCrossRef
Zurück zum Zitat Xu, Y., Vega-Guzman, J., Milovic, D., Mirzazadeh, M., Eslami, M., Mahmood, M.F., Biswas, A., Belic, M.: Bright and exotic solitons in optical metamaterials by semi-inverse variational principle. J. Nonlinear Opt. Phys. Mater. 24(04), 1550042 (2015)ADSCrossRef Xu, Y., Vega-Guzman, J., Milovic, D., Mirzazadeh, M., Eslami, M., Mahmood, M.F., Biswas, A., Belic, M.: Bright and exotic solitons in optical metamaterials by semi-inverse variational principle. J. Nonlinear Opt. Phys. Mater. 24(04), 1550042 (2015)ADSCrossRef
Zurück zum Zitat Yan, Z.: A sinh-Gordon equation expansion method to construct doubly periodic solutions for nonlinear differential equations. Chaos Solit. Fractals 16(2), 291–297 (2003)ADSMathSciNetMATHCrossRef Yan, Z.: A sinh-Gordon equation expansion method to construct doubly periodic solutions for nonlinear differential equations. Chaos Solit. Fractals 16(2), 291–297 (2003)ADSMathSciNetMATHCrossRef
Zurück zum Zitat Zafar, A., Shakeel, M., Ali, A., Akinyemi, L., Rezazadeh, H.: Optical solitons of nonlinear complex Ginzburg–Landau equation via two modified expansion schemes. Opt. Quant. Electron. 54(1), 1–15 (2022)CrossRef Zafar, A., Shakeel, M., Ali, A., Akinyemi, L., Rezazadeh, H.: Optical solitons of nonlinear complex Ginzburg–Landau equation via two modified expansion schemes. Opt. Quant. Electron. 54(1), 1–15 (2022)CrossRef
Zurück zum Zitat Zhou, Q., Zhu, Q., Liu, Y., Biswas, A., Bhrawy, A.H., Khan, K.R., Mahmood, M.F., Belic, M.: Solitons in optical metamaterials with parabolic law nonlinearity and spatio-temporal dispersion. J. Optoelectron. Adv. Mater. 16(11–12), 1221–1225 (2014) Zhou, Q., Zhu, Q., Liu, Y., Biswas, A., Bhrawy, A.H., Khan, K.R., Mahmood, M.F., Belic, M.: Solitons in optical metamaterials with parabolic law nonlinearity and spatio-temporal dispersion. J. Optoelectron. Adv. Mater. 16(11–12), 1221–1225 (2014)
Zurück zum Zitat Zhou, Q., Liu, L., Liu, Y., Yu, H., Yao, P., Wei, C., Zhang, H.: Exact optical solitons in metamaterials with cubic-quintic nonlinearity and third-order dispersion. Nonlinear Dyn. 80(3), 1365–1371 (2015)CrossRef Zhou, Q., Liu, L., Liu, Y., Yu, H., Yao, P., Wei, C., Zhang, H.: Exact optical solitons in metamaterials with cubic-quintic nonlinearity and third-order dispersion. Nonlinear Dyn. 80(3), 1365–1371 (2015)CrossRef
Metadaten
Titel
Optical solitons in metamaterials with third and fourth order dispersions
verfasst von
Thilagarajah Mathanaranjan
Dipankar Kumar
Hadi Rezazadeh
Lanre Akinyemi
Publikationsdatum
01.05.2022
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 5/2022
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-022-03656-1

Weitere Artikel der Ausgabe 5/2022

Optical and Quantum Electronics 5/2022 Zur Ausgabe