Skip to main content
Top
Published in: Optical and Quantum Electronics 4/2024

01-04-2024

Solving the relativistic Toda lattice equation via the generalized exponential rational function method

Authors: Mostafa Eslami, Samira Heidari, Sajjad A. Jedi Abduridha, Yasin Asghari

Published in: Optical and Quantum Electronics | Issue 4/2024

Log in

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

search-config
loading …

Abstract

In this article, we focus on a specific version of the NDDEs which is the relativistic Toda lattice equation. We employ the generalized exponential rational function method on a nonlinear model of surface wave propagation to recognize their diverse singular soliton and multi-soliton wave structures. What is remarkable in this article is the use of graphic diagrams, which have diversified the solutions for solving such equations, leading to a greater understanding of the movements of particles and the strengthening of nonlinear lattice dynamics. The efficiency and strength of the employed method are illustrated, signifying its applicability to a wide spectrum of NDDEs in physical phenomena.

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!

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!

Literature
go back to reference Ali, A., Ahmad, J., Javed, S., Alkarni, S., Shah, N.A.: Investigate the dynamic nature of soliton solutions and bifurcation analysis to a new generalized two-dimensional nonlinear wave equation with its stability. Results Phys. 53, 10 (2023a)CrossRef Ali, A., Ahmad, J., Javed, S., Alkarni, S., Shah, N.A.: Investigate the dynamic nature of soliton solutions and bifurcation analysis to a new generalized two-dimensional nonlinear wave equation with its stability. Results Phys. 53, 10 (2023a)CrossRef
go back to reference Arshed, S., Biswas, A., Zhou, Q., Khan, S., Adesanya, S., Moshokoa, S.P., Belic, M.: Optical solitons pertutabation with Fokas–Lenells equation by exp(\(-\phi ( )\))-expansion method. Optik 179, 341–345 (2019)CrossRefADS Arshed, S., Biswas, A., Zhou, Q., Khan, S., Adesanya, S., Moshokoa, S.P., Belic, M.: Optical solitons pertutabation with Fokas–Lenells equation by exp(\(-\phi ( )\))-expansion method. Optik 179, 341–345 (2019)CrossRefADS
go back to reference Biswas, A.: 1-soliton solution of 1+2 dimensional nonlinear Schrödinger’s equation in Kerr law media. Int. J. Theor. Phys. 48, 689–692 (2009). (3)CrossRef Biswas, A.: 1-soliton solution of 1+2 dimensional nonlinear Schrödinger’s equation in Kerr law media. Int. J. Theor. Phys. 48, 689–692 (2009). (3)CrossRef
go back to reference Ghanbari, B., Gómez-Aguilar, J.. F., Bekir, A.: Soliton solutions in the conformable (2+1)-dimensional chiral nonlinear Schrödinger equation. J. Opt. (India) 51(6), 289–316 (2022)CrossRef Ghanbari, B., Gómez-Aguilar, J.. F., Bekir, A.: Soliton solutions in the conformable (2+1)-dimensional chiral nonlinear Schrödinger equation. J. Opt. (India) 51(6), 289–316 (2022)CrossRef
go back to reference Kaplan, M., Alqahtani, R.T.: Exploration of new solitons for the fractional perturbed Radhakrishnan–Kundu–Lakshmanan model. Mathematics 11(11), 2562 (2023)CrossRef Kaplan, M., Alqahtani, R.T.: Exploration of new solitons for the fractional perturbed Radhakrishnan–Kundu–Lakshmanan model. Mathematics 11(11), 2562 (2023)CrossRef
go back to reference Kumar, D., Kaplan, M.: New analytical solutions of (2+1)-dimensional conformable time fractional Zoomeron equation via two distinct techniques. Chin. J. Phys. 56, 2173–2185 (2018a)MathSciNetCrossRef Kumar, D., Kaplan, M.: New analytical solutions of (2+1)-dimensional conformable time fractional Zoomeron equation via two distinct techniques. Chin. J. Phys. 56, 2173–2185 (2018a)MathSciNetCrossRef
go back to reference Lott, D.. A., Henriquez, A., Sturdevant, B.. J., Biswas, A.: A numerical study of optical soliton-like structures resulting from the nonlinear Schrödinger’s equation with square-root law nonlinearity. Appl. Math. Comput. 207, 319–326 (2009)MathSciNet Lott, D.. A., Henriquez, A., Sturdevant, B.. J., Biswas, A.: A numerical study of optical soliton-like structures resulting from the nonlinear Schrödinger’s equation with square-root law nonlinearity. Appl. Math. Comput. 207, 319–326 (2009)MathSciNet
go back to reference Nikan, O., Avazzadeh, Z., Kaplan, M., Alqahtani, R.T., Alharthi, N.H.: Wave propagation and stability analysis for Ostrovsky and symmetric regularized long-wave equations. Mathematics 11(9), 4030 (2023) Nikan, O., Avazzadeh, Z., Kaplan, M., Alqahtani, R.T., Alharthi, N.H.: Wave propagation and stability analysis for Ostrovsky and symmetric regularized long-wave equations. Mathematics 11(9), 4030 (2023)
go back to reference Qin, M.L., Wen, X.Y., Yuan, C.L.: Integrability, multi-soliton and rational solutions, and dynamical analysis for a relativistic Toda lattice system with one perturbation parameter. Commun. Theor. Phys. 73(5), 065003 (2021a)MathSciNetCrossRefADS Qin, M.L., Wen, X.Y., Yuan, C.L.: Integrability, multi-soliton and rational solutions, and dynamical analysis for a relativistic Toda lattice system with one perturbation parameter. Commun. Theor. Phys. 73(5), 065003 (2021a)MathSciNetCrossRefADS
go back to reference Qin, M.L., Wen, X.Y., Yuen, M.: A relativistic Toda lattice hierarchy, discrete generalized (m,2n-m)-fold Darboux transformation and diverse exact solutions. Symmetry 13, 2315 (2021b)CrossRefADS Qin, M.L., Wen, X.Y., Yuen, M.: A relativistic Toda lattice hierarchy, discrete generalized (m,2n-m)-fold Darboux transformation and diverse exact solutions. Symmetry 13, 2315 (2021b)CrossRefADS
go back to reference Rizvi, S.T., Seadawy, A.R., Ahmed, S., Younis, M., Ali, K.: Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation. Chaos Solitons Fractals 151, 111251 (2021)CrossRef Rizvi, S.T., Seadawy, A.R., Ahmed, S., Younis, M., Ali, K.: Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation. Chaos Solitons Fractals 151, 111251 (2021)CrossRef
go back to reference 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 (2014)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 (2014)MathSciNetCrossRef
go back to reference Seadawy, A.R., Iqbal, M., Lu, D.: Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsev–Petviashvili modified equal width dynamical equation. Comput. Math. Appl. 78(11), 3620–3632 (2019)MathSciNetCrossRef Seadawy, A.R., Iqbal, M., Lu, D.: Applications of propagation of long-wave with dissipation and dispersion in nonlinear media via solitary wave solutions of generalized Kadomtsev–Petviashvili modified equal width dynamical equation. Comput. Math. Appl. 78(11), 3620–3632 (2019)MathSciNetCrossRef
go back to reference Seadawy, A.R., Rizvi, S.T.R., Ahmad, S., Younis, M., Baleanu, D.: Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation. Open Phys. 19(1), 1–10 (2021)CrossRef Seadawy, A.R., Rizvi, S.T.R., Ahmad, S., Younis, M., Baleanu, D.: Lump, lump-one stripe, multiwave and breather solutions for the Hunter–Saxton equation. Open Phys. 19(1), 1–10 (2021)CrossRef
go back to reference Shah, K., Seadawy, A.R., Arfan, M.: Evaluation of one dimensional fuzzy fractional partial differential equations. Alex. Eng. J. 59(5), 3347–3353 (2020)CrossRef Shah, K., Seadawy, A.R., Arfan, M.: Evaluation of one dimensional fuzzy fractional partial differential equations. Alex. Eng. J. 59(5), 3347–3353 (2020)CrossRef
go back to reference Wang, J., Shehzad, K., Seadawy, A.R., Arshad, M., Asmat, F.: Dynamic study of multi-peak solitons and other wave solutions of new coupled KdV and new coupled Zakharov–Kuznetsov systems with their stability. J. Taibah Univ. Sci. 17(1), 2163872 (2023a)CrossRef Wang, J., Shehzad, K., Seadawy, A.R., Arshad, M., Asmat, F.: Dynamic study of multi-peak solitons and other wave solutions of new coupled KdV and new coupled Zakharov–Kuznetsov systems with their stability. J. Taibah Univ. Sci. 17(1), 2163872 (2023a)CrossRef
go back to reference Wang, X., Ehsan, H., Abbas, M., Akram, G., Sadaf, M., Abdeljawad, T.: Analytical solitary wave solutions of a time-fractional thin-film ferroelectric material equation involving beta-derivative using modified auxiliary equation method. Results Phys. 48, 106411 (2023b)CrossRef Wang, X., Ehsan, H., Abbas, M., Akram, G., Sadaf, M., Abdeljawad, T.: Analytical solitary wave solutions of a time-fractional thin-film ferroelectric material equation involving beta-derivative using modified auxiliary equation method. Results Phys. 48, 106411 (2023b)CrossRef
go back to reference Yang, D., Jiang, X.: Line-soliton, lump and interaction solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equation with time-dependent via hirota bilinear forms. Results Phys. 53(10), 106904 (2023)CrossRef Yang, D., Jiang, X.: Line-soliton, lump and interaction solutions to the (2+1)-dimensional Hirota–Satsuma–Ito equation with time-dependent via hirota bilinear forms. Results Phys. 53(10), 106904 (2023)CrossRef
go back to reference Younas, U., Seadawy, A.R., Younis, M., Rizvi, S.: Optical solitons and closed form solutions to the (3+ 1)-dimensional resonant Schrödinger dynamical wave equation. Int. J. Mod. Phys.B 34(30), 2050291 (2020)CrossRefADS Younas, U., Seadawy, A.R., Younis, M., Rizvi, S.: Optical solitons and closed form solutions to the (3+ 1)-dimensional resonant Schrödinger dynamical wave equation. Int. J. Mod. Phys.B 34(30), 2050291 (2020)CrossRefADS
Metadata
Title
Solving the relativistic Toda lattice equation via the generalized exponential rational function method
Authors
Mostafa Eslami
Samira Heidari
Sajjad A. Jedi Abduridha
Yasin Asghari
Publication date
01-04-2024
Publisher
Springer US
Published in
Optical and Quantum Electronics / Issue 4/2024
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-023-06108-6

Other articles of this Issue 4/2024

Optical and Quantum Electronics 4/2024 Go to the issue