Skip to main content
Erschienen in: Optical and Quantum Electronics 5/2024

01.05.2024

Soliton solutions of (2+1) complex modified Korteweg–de Vries system using improved Sardar method

verfasst von: Umar Ali Muhammad, Jamilu Sabi’u, Soheil Salahshour, Hadi Rezazadeh

Erschienen in: Optical and Quantum Electronics | Ausgabe 5/2024

Einloggen

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

search-config
loading …

Abstract

This paper investigates (2+1)-dimensional complex modified Korteweg–de Vries (cmKdV) system equations using the improved Sadar subequation method. It uncovers analytical solutions, including dark solitons, bright solitons, and periodic waves. The dynamic behavior of these solutions is illustrated through 2D and 3D plots by adjusting parameters. The results highlight the effectiveness and simplicity of the proposed methods, providing a versatile approach to obtaining various traveling wave solutions. These findings are expected to advance the shallow water theory of ideal fluids.

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 Ahmad, J., Mustafa, Z., Turki, N.B., Shah, N.A.: Solitary wave structures for the stochastic Nizhnik–Novikov–Veselov system via modified generalized rational exponential function method. Res. Phys. 52, 106776 (2023) Ahmad, J., Mustafa, Z., Turki, N.B., Shah, N.A.: Solitary wave structures for the stochastic Nizhnik–Novikov–Veselov system via modified generalized rational exponential function method. Res. Phys. 52, 106776 (2023)
Zurück zum Zitat Alquran, M., Jaradat, I.: Multiplicative of dual-waves generated upon increasing the phase velocity parameter embedded in dual-mode Schrödinger with nonlinearity Kerr laws. Nonlinear Dyn. 96, 115–121 (2019)CrossRef Alquran, M., Jaradat, I.: Multiplicative of dual-waves generated upon increasing the phase velocity parameter embedded in dual-mode Schrödinger with nonlinearity Kerr laws. Nonlinear Dyn. 96, 115–121 (2019)CrossRef
Zurück zum Zitat Alquran, M., Jaradat, I., Yusuf, A., Sulaiman, T.A.: Heart-cusp and bell-shaped-cusp optical solitons for an extended two-mode version of the complex Hirota model: application in optics. Opt. Quant. Electron. 53, 1–13 (2021)CrossRef Alquran, M., Jaradat, I., Yusuf, A., Sulaiman, T.A.: Heart-cusp and bell-shaped-cusp optical solitons for an extended two-mode version of the complex Hirota model: application in optics. Opt. Quant. Electron. 53, 1–13 (2021)CrossRef
Zurück zum Zitat Arshed, S., Raza, N.: Optical solitons perturbation of Fokas–Lenells equation with full nonlinearity and dual dispersion. Chin. J. Phys. 63, 314–324 (2020)MathSciNetCrossRef Arshed, S., Raza, N.: Optical solitons perturbation of Fokas–Lenells equation with full nonlinearity and dual dispersion. Chin. J. Phys. 63, 314–324 (2020)MathSciNetCrossRef
Zurück zum Zitat Atilgan, E., Senol, M., Kurt, A., Tasbozan, O.: New wave solutions of time-fractional coupled Boussinesq–Whitham–Broer–Kaup equation as a model of water waves. China Ocean Eng. 33, 477–483 (2019)CrossRefADS Atilgan, E., Senol, M., Kurt, A., Tasbozan, O.: New wave solutions of time-fractional coupled Boussinesq–Whitham–Broer–Kaup equation as a model of water waves. China Ocean Eng. 33, 477–483 (2019)CrossRefADS
Zurück zum Zitat Dong, S.H.: Wave Equations in Higher Dimensions. Springer Science Business Media, Berlin/Heidelberg (2011)CrossRef Dong, S.H.: Wave Equations in Higher Dimensions. Springer Science Business Media, Berlin/Heidelberg (2011)CrossRef
Zurück zum Zitat Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S.S.: Exact solutions to the space–time fractional Schrödinger–Hirota equation and the space–time modified KDV–Zakharov–Kuznetsov equation. Opt. Quant. Electron. 49, 1–15 (2017)CrossRef Eslami, M., Rezazadeh, H., Rezazadeh, M., Mosavi, S.S.: Exact solutions to the space–time fractional Schrödinger–Hirota equation and the space–time modified KDV–Zakharov–Kuznetsov equation. Opt. Quant. Electron. 49, 1–15 (2017)CrossRef
Zurück zum Zitat Iqbal, M., Seadawy, A.R.: Instability of modulation wave train and disturbance of time period in slightly stable media for unstable nonlinear Schrödinger dynamical equation. Mod. Phys. Lett. B 34(supp01), 2150010 (2020)CrossRefADS Iqbal, M., Seadawy, A.R.: Instability of modulation wave train and disturbance of time period in slightly stable media for unstable nonlinear Schrödinger dynamical equation. Mod. Phys. Lett. B 34(supp01), 2150010 (2020)CrossRefADS
Zurück zum Zitat Iqbal, M., Seadawy, A.R., Lu, D.: Construction of solitary wave solutions to the nonlinear modified Kortewege–de Vries dynamical equation in unmagnetized plasma via mathematical methods. Mod. Phys. Lett. A 33(32), 1850183 (2018)MathSciNetCrossRefADS Iqbal, M., Seadawy, A.R., Lu, D.: Construction of solitary wave solutions to the nonlinear modified Kortewege–de Vries dynamical equation in unmagnetized plasma via mathematical methods. Mod. Phys. Lett. A 33(32), 1850183 (2018)MathSciNetCrossRefADS
Zurück zum Zitat Justin, M., David, V., Shahen, N.H.M., Sylvere, A.S., Rezazadeh, H., Inc, M., et al.: Sundry optical solitons and modulational instability in Sasa–Satsuma model. Opt. Quantum Electron. 54, 1–15 (2022)CrossRef Justin, M., David, V., Shahen, N.H.M., Sylvere, A.S., Rezazadeh, H., Inc, M., et al.: Sundry optical solitons and modulational instability in Sasa–Satsuma model. Opt. Quantum Electron. 54, 1–15 (2022)CrossRef
Zurück zum Zitat Khan, M.I., Asghar, S., Sabi’u, J.: Jacobi elliptic function expansion method for the improved modified Kortwedge–de Vries equation. Opt. Quantum Electron. 54(11), 734 (2022)CrossRef Khan, M.I., Asghar, S., Sabi’u, J.: Jacobi elliptic function expansion method for the improved modified Kortwedge–de Vries equation. Opt. Quantum Electron. 54(11), 734 (2022)CrossRef
Zurück zum Zitat Khater, M.M., Park, C., Lu, D., Attia, R.A.: Analytical, semi-analytical, and numerical solutions for the Cahn–Allen equation. Adv. Difference Equ. 2020(1), 9 (2020a)MathSciNetCrossRef Khater, M.M., Park, C., Lu, D., Attia, R.A.: Analytical, semi-analytical, and numerical solutions for the Cahn–Allen equation. Adv. Difference Equ. 2020(1), 9 (2020a)MathSciNetCrossRef
Zurück zum Zitat Khater, M.M., Attia, R.A., Lu, D.: Computational and numerical simulations for the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation. Phys. Scr. 95(5), 055213 (2020b)CrossRefADS Khater, M.M., Attia, R.A., Lu, D.: Computational and numerical simulations for the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation. Phys. Scr. 95(5), 055213 (2020b)CrossRefADS
Zurück zum Zitat Kurt, A.: New analytical and numerical results for fractional Bogoyavlensky–Konopelchenko equation arising in fluid dynamics. Appl. Math. A J. Chin. Univ. 35, 101–112 (2020)MathSciNetCrossRef Kurt, A.: New analytical and numerical results for fractional Bogoyavlensky–Konopelchenko equation arising in fluid dynamics. Appl. Math. A J. Chin. Univ. 35, 101–112 (2020)MathSciNetCrossRef
Zurück zum Zitat Raza, N., Zubair, A.: Bright, dark and dark-singular soliton solutions of nonlinear Schrödinger’s equation with spatio–temporal dispersion. J. Mod. Opt. 65(17), 1975–1982 (2018)CrossRefADS Raza, N., Zubair, A.: Bright, dark and dark-singular soliton solutions of nonlinear Schrödinger’s equation with spatio–temporal dispersion. J. Mod. Opt. 65(17), 1975–1982 (2018)CrossRefADS
Zurück zum Zitat Raza, N., Arshed, S., Sial, S.: Optical solitons for coupled Fokas–Lenells equation in birefringence fibers. Mod. Phys. Lett. B 33(26), 1950317 (2019)MathSciNetCrossRefADS Raza, N., Arshed, S., Sial, S.: Optical solitons for coupled Fokas–Lenells equation in birefringence fibers. Mod. Phys. Lett. B 33(26), 1950317 (2019)MathSciNetCrossRefADS
Zurück zum Zitat Rehman, S.U., Bilal, M., Ahmad, J.: The study of solitary wave solutions to the time conformable Schrödinger system by a powerful computational technique. Opt. Quant. Electron. 54(4), 228 (2022a)CrossRef Rehman, S.U., Bilal, M., Ahmad, J.: The study of solitary wave solutions to the time conformable Schrödinger system by a powerful computational technique. Opt. Quant. Electron. 54(4), 228 (2022a)CrossRef
Zurück zum Zitat Rehman, S.U., Ahmad, J., Muhammad, T.: Dynamics of novel exact soliton solutions to stochastic chiral nonlinear Schrödinger equation. Alex. Eng. J. 79, 568–580 (2023a)CrossRef Rehman, S.U., Ahmad, J., Muhammad, T.: Dynamics of novel exact soliton solutions to stochastic chiral nonlinear Schrödinger equation. Alex. Eng. J. 79, 568–580 (2023a)CrossRef
Zurück zum Zitat Rezazadeh, H., Mirhosseini-Alizamini, S.M., Eslami, M., Rezazadeh, M., Mirzazadeh, M., Abbagari, S.: New optical solitons of nonlinear conformable fractional Schrödinger–Hirota equation. Optik 172, 545–553 (2018)CrossRefADS Rezazadeh, H., Mirhosseini-Alizamini, S.M., Eslami, M., Rezazadeh, M., Mirzazadeh, M., Abbagari, S.: New optical solitons of nonlinear conformable fractional Schrödinger–Hirota equation. Optik 172, 545–553 (2018)CrossRefADS
Zurück zum Zitat Russell, J. S.: Report on Waves: made to the meetings of the British Association in 1842–43. Printed by Richard and John E. Taylor, London (1845) Russell, J. S.: Report on Waves: made to the meetings of the British Association in 1842–43. Printed by Richard and John E. Taylor, London (1845)
Zurück zum Zitat Sabi’u, J., Jibril, A., Gadu, A.M.: New exact solution for the (3+1) conformable space–time fractional modified Korteweg–de-Vries equations via sine–cosine method. J. Taibah Univ. Sci. 13(1), 91–95 (2019)CrossRef Sabi’u, J., Jibril, A., Gadu, A.M.: New exact solution for the (3+1) conformable space–time fractional modified Korteweg–de-Vries equations via sine–cosine method. J. Taibah Univ. Sci. 13(1), 91–95 (2019)CrossRef
Zurück zum Zitat Sabi’u, J., Inc, M., Leta, T.D., Baleanu, D., Rezazadeh, H.: Dynamical behaviour of the Joseph–Egri equation. Therm. Sci. 27(Spec. issue 1), 19–28 (2023)CrossRef Sabi’u, J., Inc, M., Leta, T.D., Baleanu, D., Rezazadeh, H.: Dynamical behaviour of the Joseph–Egri equation. Therm. Sci. 27(Spec. issue 1), 19–28 (2023)CrossRef
Zurück zum Zitat Seadawy, A.R.: Stability analysis for two-dimensional ion-acoustic waves in quantum plasmas. Phys. Plasmas 10(1063/1), 4875987 (2014a) Seadawy, A.R.: Stability analysis for two-dimensional ion-acoustic waves in quantum plasmas. Phys. Plasmas 10(1063/1), 4875987 (2014a)
Zurück zum Zitat Seadawy, A.R.: Stability analysis for Zakharov–Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma. Comput. Math. Appl. 67(1), 172–180 (2014b)MathSciNetCrossRef Seadawy, A.R.: Stability analysis for Zakharov–Kuznetsov equation of weakly nonlinear ion-acoustic waves in a plasma. Comput. Math. Appl. 67(1), 172–180 (2014b)MathSciNetCrossRef
Zurück zum Zitat Seadawy, A.R., Iqbal, M.: Optical soliton solutions for nonlinear complex Ginzburg–Landau dynamical equation with laws of nonlinearity Kerr law media. Int. J. Mod. Phys. B 34(19), 2050179 (2020)MathSciNetCrossRefADS Seadawy, A.R., Iqbal, M.: Optical soliton solutions for nonlinear complex Ginzburg–Landau dynamical equation with laws of nonlinearity Kerr law media. Int. J. Mod. Phys. B 34(19), 2050179 (2020)MathSciNetCrossRefADS
Zurück zum Zitat Seadawy, A.R., Lu, D.: Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma. Res. Phys. 6, 590–593 (2016) Seadawy, A.R., Lu, D.: Ion acoustic solitary wave solutions of three-dimensional nonlinear extended Zakharov–Kuznetsov dynamical equation in a magnetized two-ion-temperature dusty plasma. Res. Phys. 6, 590–593 (2016)
Zurück zum Zitat Seadawy, A.R., Iqbal, M., Lu, D.: Analytical methods via bright–dark solitons and solitary wave solutions of the higher-order nonlinear Schrödinger equation with fourth-order dispersion. Mod. Phys. Lett. B 33(35), 1950443 (2019)CrossRefADS Seadawy, A.R., Iqbal, M., Lu, D.: Analytical methods via bright–dark solitons and solitary wave solutions of the higher-order nonlinear Schrödinger equation with fourth-order dispersion. Mod. Phys. Lett. B 33(35), 1950443 (2019)CrossRefADS
Zurück zum Zitat Shahen, N.H.M., Foyjonnesa, Bashar, M.H., Tahseen, T., Hossain, S.: Solitary and rogue wave solutions to the conformable time fractional modified Kawahara equation in mathematical physics. Adv. Math. Phys. 2021, 1–9 (2021)MathSciNetCrossRef Shahen, N.H.M., Foyjonnesa, Bashar, M.H., Tahseen, T., Hossain, S.: Solitary and rogue wave solutions to the conformable time fractional modified Kawahara equation in mathematical physics. Adv. Math. Phys. 2021, 1–9 (2021)MathSciNetCrossRef
Zurück zum Zitat Shaikhova, G., Serikbayev, N., Yesmakhanova, K., Myrzakulov, R.: Nonlocal complex modified Korteweg–de Vries equations: Reductions and exact solutions. In: Proceedings of the Twenty-First International Conference on Geometry, Integrability and Quantization, vol. 21, pp. 265–272. Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy (2020). https://doi.org/10.7546/giq-21-2020-265-271 Shaikhova, G., Serikbayev, N., Yesmakhanova, K., Myrzakulov, R.: Nonlocal complex modified Korteweg–de Vries equations: Reductions and exact solutions. In: Proceedings of the Twenty-First International Conference on Geometry, Integrability and Quantization, vol. 21, pp. 265–272. Bulgarian Academy of Sciences, Institute for Nuclear Research and Nuclear Energy (2020). https://​doi.​org/​10.​7546/​giq-21-2020-265-271
Zurück zum Zitat Solitons, M.A.P.C.: Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge (1991) Solitons, M.A.P.C.: Nonlinear Evolution Equations and Inverse Scattering. Cambridge University Press, Cambridge (1991)
Zurück zum Zitat 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 91, 1–8 (2018)CrossRef 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 91, 1–8 (2018)CrossRef
Zurück zum Zitat Tahir, M., Awan, A.U., Rehman, H.U.: Dark and singular optical solitons to the Biswas–Arshed model with Kerr and power law nonlinearity. Optik 185, 777–783 (2019)CrossRefADS Tahir, M., Awan, A.U., Rehman, H.U.: Dark and singular optical solitons to the Biswas–Arshed model with Kerr and power law nonlinearity. Optik 185, 777–783 (2019)CrossRefADS
Zurück zum Zitat Tao, G., Sabi’u, J., Nestor, S., El-Shiekh, R.M., Akinyemi, L., Az-Zo’bi, E., Betchewe, G.: Dynamics of a new class of solitary wave structures in telecommunications systems via a (2+1)-dimensional nonlinear transmission line. Mod. Phys. Lett. B 36(19), 2150596 (2022)MathSciNetCrossRefADS Tao, G., Sabi’u, J., Nestor, S., El-Shiekh, R.M., Akinyemi, L., Az-Zo’bi, E., Betchewe, G.: Dynamics of a new class of solitary wave structures in telecommunications systems via a (2+1)-dimensional nonlinear transmission line. Mod. Phys. Lett. B 36(19), 2150596 (2022)MathSciNetCrossRefADS
Zurück zum Zitat Tozar, A., Kurt, A., Tasbozan, O.: New wave solutions of an integrable dispersive wave equation with a fractional time derivative arising in ocean engineering models. Kuwait J. Sci. 47(2), 22–33 (2020). Tozar, A., Kurt, A., Tasbozan, O.: New wave solutions of an integrable dispersive wave equation with a fractional time derivative arising in ocean engineering models. Kuwait J. Sci. 47(2), 22–33 (2020).
Zurück zum Zitat Zabusky, N.J., Kruskal, M.D.: Interaction of solitons in a collision less plasma and the recurrence of initial states. Phys. Rev. Lett. 15(6), 240 (1965)CrossRefADS Zabusky, N.J., Kruskal, M.D.: Interaction of solitons in a collision less plasma and the recurrence of initial states. Phys. Rev. Lett. 15(6), 240 (1965)CrossRefADS
Zurück zum Zitat Zubair, A., Raza, N.: Bright and dark solitons in (n+1)-dimensions with spatio–temporal dispersion. J. Opt. 48, 594–605 (2019)CrossRef Zubair, A., Raza, N.: Bright and dark solitons in (n+1)-dimensions with spatio–temporal dispersion. J. Opt. 48, 594–605 (2019)CrossRef
Metadaten
Titel
Soliton solutions of (2+1) complex modified Korteweg–de Vries system using improved Sardar method
verfasst von
Umar Ali Muhammad
Jamilu Sabi’u
Soheil Salahshour
Hadi Rezazadeh
Publikationsdatum
01.05.2024
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 5/2024
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-024-06591-5

Weitere Artikel der Ausgabe 5/2024

Optical and Quantum Electronics 5/2024 Zur Ausgabe

Neuer Inhalt