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Erschienen in: Optical and Quantum Electronics 4/2024

01.04.2024

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

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

Erschienen in: Optical and Quantum Electronics | Ausgabe 4/2024

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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.

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Literatur
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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)
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
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 (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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Zurück zum Zitat 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
Metadaten
Titel
Solving the relativistic Toda lattice equation via the generalized exponential rational function method
verfasst von
Mostafa Eslami
Samira Heidari
Sajjad A. Jedi Abduridha
Yasin Asghari
Publikationsdatum
01.04.2024
Verlag
Springer US
Erschienen in
Optical and Quantum Electronics / Ausgabe 4/2024
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI
https://doi.org/10.1007/s11082-023-06108-6

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