Top

Optical and Quantum Electronics

Published in:

01-04-2023

Extraction of soliton waves from the longitudinal wave equation with local M-truncated derivatives

Authors: Neslihan Ozdemir, Aydin Secer, Mustafa Bayram

Published in: Optical and Quantum Electronics | Issue 4/2023

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

search-config

AI-assisted search

Off

Abstract

We have extracted some soliton solutions of the fractional longitudinal wave equation with the M-truncated derivative (M-LWE), which emerges in a magneto electro-elastic circular rod. To obtain new results of this model, the unified Riccati equation expansion and new Kudryashov methods have been utilized for the first time. The presented methods have been productively implemented to the considered model. With the help of these two methods, new soliton waves of the M-LWE have been obtained successfully. For a better understanding of the subject and analysis of the results, 3D, contour, and 2D graphs of some soliton solutions have been presented. The interesting part of our work is that both methods, named unified Riccati equation expansion and the new Kudryashov methods have successfully been applied for the first time to get new soliton solutions of M-LWE.

previous article A novel rhombic shaped photonic crystal bio-sensor for identifying disorders in the blood samples

next article Design and simulation of an all-optical priority encoder based on 2-D photonic crystal

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

Akbar, M.A., Akinyemi, L., Yao, S.-W., Jhangeer, A., Rezazadeh, H., Khater, M.M., Ahmad, H., Inc, M.: Soliton solutions to the Boussinesq equation through Sine–Gordon method and Kudryashov method. Results Phys. 25, 104228 (2021)CrossRef

Akinyemi, L., Morazara, E.: Integrability, multi-solitons, breathers, lumps and wave interactions for generalized extended Kadomtsev–Petviashvili equation. Nonlinear Dyn. 111, 4683–4707 (2023)

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., Az-Zo’bi, E., Veeresha, P., Akpan, U.: Novel soliton solutions of four sets of generalized (2+ 1)-dimensional Boussinesq–Kadomtsev–Petviashvili-like equations. Mod. Phys. Lett. B 36(01), 2150530 (2022)MathSciNetCrossRefADS

Aljahdaly, N.H., ALoufi, R.G., Seadawy, A.R.: Stability analysis and soliton solutions for the longitudinal wave equation in magneto electro-elastic circular rod. Results Phys. 26, 104329 (2021)CrossRef

Alquran, M., Alhami, R.: Convex-periodic, kink-periodic, Peakon–Soliton and kink bidirectional wave-solutions to new established two-mode generalization of Cahn–Allen equation. Results Phys. 34, 105257 (2022)CrossRef

Alquran, M., Jaradat, I., Baleanu, D.: Shapes and dynamics of dual-mode Hirota–Satsuma coupled kdv equations: exact traveling wave solutions and analysis. Chin. J. Phys. 58, 49–56 (2019)MathSciNetCrossRef

Baskonus, H., Gómez-Aguilar, J.: New singular soliton solutions to the longitudinal wave equation in a magneto-electro-elastic circular rod with m-derivative. Mod. Phys. Lett. B 33(21), 1950251 (2019)MathSciNetCrossRefADS

Biswas, A., Ekici, M., Sonmezoglu, A., Belic, M.R.: Highly dispersive optical solitons with Kerr law nonlinearity by f-expansion. Optik 181, 1028–1038 (2019)CrossRefADS

Cinar, M., Onder, I., Secer, A., Yusuf, A., Sulaiman, T.A., Bayram, M., Aydin, H.: The analytical solutions of Zoomeron equation via extended rational sin-cos and sinh–cosh methods. Phys. Scr. 96(9), 094002 (2021)CrossRefMATHADS

Esen, H., Ozisik, M., Secer, A., Bayram, M.: Optical soliton perturbation with Fokas–Lenells equation via enhanced modified extended tanh-expansion approach. Optik 267, 169615 (2022)CrossRefADS

Guo, S., Mei, L., Zhou, Y., Li, C.: The extended Riccati equation mapping method for variable-coefficient diffusion–reaction and mkdv equations. Appl. Math. Comput. 217(13), 6264–6272 (2011)MathSciNetMATH

Habiba, U., Salam, M.A., Hossain, M.B., Datta, M.: Solitary wave solutions of Chafee–Infante equation and (2+ 1)-dimensional breaking soliton equation by the improved Kudryashov method. Glob. J. Sci. Front. Res. 19(5), 1–9 (2019)

Hosseini, K., Mayeli, P., Bejarbaneh, E.Y., Zhou, Q.: New optical solitons of the longitudinal wave equation in a magnetoelectro-elastic circular rod. Acta Phys. Pol. A 133, 20–22 (2018)CrossRefADS

Hosseini, K., Salahshour, S., Mirzazadeh, M.: Bright and dark solitons of a weakly nonlocal schrödinger equation involving the parabolic law nonlinearity. Optik 227, 166042 (2021)CrossRefADS

Kudryashov, N.A.: Method for finding highly dispersive optical solitons of nonlinear differential equations. Optik 206, 163550 (2020)CrossRefADS

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

Li, Z., Dai, Z.: Abundant new exact solutions for the (3+ 1)-dimensional Jimbo–Miwa equation. J. Math. Anal. Appl. 361(2), 587–590 (2010)MathSciNetCrossRefMATH

Ma, X., Pan, Y., Chang, L.: Explicit travelling wave solutions in a magneto-electro-elastic circular rod. Int. J. Comput. Sci. Issues 10(1), 62 (2013)

Malik, S., Kumar, S., Das, A.: A (2+ 1)-dimensional combined kdv-mkdv equation: integrability, stability analysis and soliton solutions. Nonlinear Dyn. 107(3), 2689–2701 (2022)CrossRef

Malik, S., Hashemi, M.S., Kumar, S., Rezazadeh, H., Mahmoud, W., Osman, M.: Application of new Kudryashov method to various nonlinear partial differential equations. Opt. Quant. Electron. 55(1), 1–13 (2023)CrossRef

Ntiamoah, D., Ofori-Atta, W., Akinyemi, L.: The higher-order modified Korteweg-de Vries equation. Its soliton, breather and approximate solutions. J. Ocean Eng. Sci. (in press) (2022)

Ozdemir, N., Esen, H., Secer, A., Bayram, M., Yusuf, A., Sulaiman, T.A.: Optical soliton solutions to Chen Lee Liu model by the modified extended tanh expansion scheme. Optik 245, 167643 (2021)CrossRefADS

Ozdemir, N., Secer, A., Ozisik, M., Bayram, M.: Perturbation of dispersive optical solitons with schrödinger–Hirota equation with Kerr law and spatio-temporal dispersion. Optik 265, 169545 (2022)CrossRefADS

Ozisik, M., Secer, A., Bayram, M.: The bell-shaped perturbed dispersive optical solitons of Biswas–Arshed equation using the new Kudryashov’s approach. Optik 267, 169650 (2022)CrossRefADS

Rezazadeh, H., Ullah, N., Akinyemi, L., Shah, A., Mirhosseini-Alizamin, S.M., Chu, Y.-M., Ahmad, H.: Optical soliton solutions of the generalized non-autonomous nonlinear Schrödinger equations by the new kudryashov’s method. Results Phys. 24, 104179 (2021)CrossRef

Seadawy, A.R., Manafian, J.: New soliton solution to the longitudinal wave equation in a magneto-electro-elastic circular rod. Results Phys. 8, 1158–1167 (2018)CrossRefADS

Sirendaoreji: Unified Riccati equation expansion method and its application to two new classes of Benjamin–Bona–Mahony equations. Nonlinear Dyn. 89(1), 333–344 (2017)MathSciNetCrossRefMATH

Sousa, J., de Oliveira, E.C.: A new truncated m-fractional derivative type unifying some fractional derivative types with classical properties (2017). arXiv preprint arXiv:1704.08187

Xue, C., Pan, E., Zhang, S.: Solitary waves in a magneto-electro-elastic circular rod. Smart Mater. Struct. 20(10), 105010 (2011)CrossRefADS

Yépez-Martínez, H., Gómez-Aguilar, J.: Local m-derivative of order \(\alpha \) and the modified expansion function method applied to the longitudinal wave equation in a magneto electro-elastic circular rod. Opt. Quant. Electron. 50(10), 1–11 (2018)CrossRef

Zhao, Y.-H., Mathanaranjan, T., Rezazadeh, H., Akinyemi, L., Inc, M.: New solitary wave solutions and stability analysis for the generalized (3+ 1)-dimensional nonlinear wave equation in liquid with gas bubbles. Results Phys. 43, 106083 (2022)CrossRef

Zhu, S.-D.: The generalizing Riccati equation mapping method in non-linear evolution equation: application to (2+ 1)-dimensional Boiti–Leon–Pempinelle equation. Chaos Solitons Fractals 37(5), 1335–1342 (2008)MathSciNetCrossRefMATHADS

Title: Extraction of soliton waves from the longitudinal wave equation with local M-truncated derivatives
Authors: Neslihan Ozdemir
Aydin Secer
Mustafa Bayram
Publication date: 01-04-2023
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 4/2023
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-023-04570-w

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 4/2023

Design and numerical analysis of high-performance all-optical 4 × 2 encoder using photonic crystal ring resonator

Enhancing the parameters of ZnO/CdZnS thin film photodetector by thermal annealing

First-principles study of electronic and optical properties of CdxMg1 − xO alloys, TB-mBJ calculations

Investigation of the reorientation of the liquid crystal molecules under the influence of the dye torque

Design and simulation of reconfigurable optical logic gates for integrated optical circuits

Investigation of the electronic and optical activity of halogen-substituted 2-nitrotoulene by density functional theory