nach oben

Optical and Quantum Electronics

Erschienen in:

01.08.2023

Stability analysis and dynamical behavior of solitons in nonlinear optics modelled by Lakshmanan–Porsezian–Daniel equation

verfasst von: Sonia Akram, Jamshad Ahmad, Shafqat-Ur Rehman

Erschienen in: Optical and Quantum Electronics | Ausgabe 8/2023

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

The current research analyses several new optical solitons solutions to the Lakshmanan–Porsezian–Daniel (LPD) equation with the Kerr law of nonlinearity which arises from the application of the Heisenberg spin chain and fiber optics, via two modified analytical methodologies. The auxiliary equation method (AE) and improved F-expansion method are used to derive several accurate solitary wave solutions of the LPD model. The key objectives of the study are in two folds. Firstly, the implementation of these schemes yields dark, bright, multi-wave, singular, alphabetic and exotic solitons solutions to the model. Secondly, we discuss the stability analysis of our selected model which confirms that the governing model is stable. For understanding the physical configuration of some constructed solitons, we plotted 2D, 3D, contours and density graphs. These solutions secured in this study will play a vital role to understand the exact dynamics of nonlinear phenomena in nonlinear optics and also enhance the previously established results. In the present era of communications network technology and nonlinear optics, the employed techniques seem to be a more categorical, influential and proficient approaches for securing optical solutions to several diversified contemporary models.

Vorheriger Artikel Analysis of the behavior of pulsed vortex beams in oceanic turbulence

Nächster Artikel An ultra high capacity polarization division multiplexed 128-QAM radio over fiber (RoF) system

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!

Jetzt informieren

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!

Jetzt informieren

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!

Jetzt informieren

Adeyemo, O.D., Khalique, C.M.: Analytic solutions and conservation laws of a (2+ 1)-dimensional generalized Yu–Toda–Sasa–Fukuyama equation. Chin. J. Phys. 77, 927–944 (2022)MathSciNet

Adeyemo, O.D., Zhang, L., Khalique, C.M.: Bifurcation theory, lie group-invariant solutions of subalgebras and conservation laws of a generalized (2+ 1)-dimensional BK equation type II in plasma physics and fluid mechanics. Mathematics 10(14), 2391 (2022)

Aggarwal, S., Sharma, N., Chauhan, R.: Application of Kamal transform for solving linear volterra integral equations of first kind. Int. J. Res. Advent Technol. 6(8), 2081–2088 (2018)

Ahmad, J.: Dynamics of optical and other soliton solutions in fiber bragg gratings with Kerr law and stability analysis. Arab. J. Sci. Eng. 48(1), 803–819 (2023)

Akbar, M.A., Wazwaz, A.M., Mahmud, F., Baleanu, D., Roy, R., Barman, H.K., Osman, M.S.: Dynamical behavior of solitons of the perturbed nonlinear Schrödinger equation and microtubules through the generalized Kudryashov scheme. Results Phys. 43, 106079 (2022)

Akbulut, A., Islam, R., Arafat, Y., Taçcan, F.: A novel scheme for SMCH equation with two different approaches. Comput. Methods Differ. Equ. 11, 263–280 (2022)MathSciNetMATH

Akram, S., Ahmad, J., Rehman, S., U., Sarwar, S., Ali, A.: Dynamics of soliton solutions in optical fibers modelled by perturbed nonlinear Schrödinger equation and stability analysis. Opt. Quant. Electron. 55, 450 (2023)

Akram, G., Sadaf, M., Arshed, S., Sameen, F.: Bright, dark, kink, singular and periodic soliton solutions of Lakshmanan–Porsezian–Daniel model by generalized projective Riccati equations method. Optik 241, 167051 (2021)ADS

Al Qarni, A., Banaja, M.A., Bakodah, H.O., Alshaery, A.A., Zhou, Q., Biswas, A., Belic, M.R.: Bright optical solitons for Lakshmanan–Porsezian–Daniel model with spatio-temporal dispersion by improved Adomian decomposition method. Optik 181, 891–897 (2019)ADS

Alzahrani, A.K., Belic, M.R.: Cubic-quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by semi-inverse variational principle. Ukr. J. Phys. Opt. 22, 123 (2021)

Anjum, N., He, J.H.: Laplace transform: making the variational iteration method easier. Appl. Math. Lett. 92, 134–138 (2019)MathSciNetMATH

Asghari, Y., Eslami, M., Rezazadeh, H.: Exact solutions to the conformable time-fractional discretized mKdv lattice system using the fractional transformation method. Opt. Quant. Electron. 55(4), 318 (2023)

Asghari, Y., Eslami, M., Rezazadeh, H.: Soliton solutions for the time-fractional nonlinear differential-difference equation with conformable derivatives in the ferroelectric materials. Opt. Quant. Electron. 55(4), 289 (2023)

Asjad, M.I., Inc, M., Faridi, W.A., Bakar, M.A., Muhammad, T., Rezazadeh, H.: Optical solitonic structures with singular and non-singular kernel for nonlinear fractional model in quantum mechanics. Opt. Quant. Electron. 55(3), 1–20 (2023)

Bashar, M.H., Arafat, S.Y., Islam, S.R., Islam, S., Rahman, M.M.: Extraction of some optical solutions to the (2+ 1)-dimensional Kundu–Mukherjee–Naskar equation by two efficient approaches. Partial Differ. Equ. Appl. Math. 6, 100404 (2022)

Bashar, M.H., Arafat, S.Y., Islam, S.R., Rahman, M.M.: Wave solutions of the couple Drinfel’d–Sokolov–Wilson equation: new wave solutions and free parameters effect. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.05.003CrossRef

Bashar, M.H., Inc, M., Islam, S.R., Mahmoud, K.H., Akbar, M.A.: Soliton solutions and fractional effects to the time-fractional modified equal width equation. Alex. Eng. J. 61(12), 12539–12547 (2022)

Biazar, J., Ayati, Z.: Improved G’/G-expansion method and comparing with tanh-coth method. Appl. Appl. Math. Int. J. (AAM) 6(1), 20 (2011)MathSciNetMATH

Bilal, M., Ahmad, J.: Dynamics of soliton solutions in saturated ferromagnetic materials by a novel mathematical method. J Magn. Magn. Mater. 538, 168245 (2021). https://doi.org/10.1016/j.jmmm.2021.168245CrossRef

Bilal, M., Ahmad, J.: Dispersive solitary wave solutions for the dynamical soliton model by three versatile analytical mathematical methods. Eur. Phys. J. Plus 137(6), 674 (2022). https://doi.org/10.1140/epjp/s13360-022-02897-zCrossRef

Bilal, M., Younas, U., Yusuf, A., Sulaiman, T.A., Bayram, M.: Optical solitons with the birefringent fibers without four-wave mixing via the Lakshmanan–Porsezian–Daniel equation. Optik 243, 167489 (2021). https://doi.org/10.1016/j.ijleo.2021.167489ADSCrossRef

Bilal, M., Rehman, S.U., Ahamd, J.: Investigation of optical solitons and modulation instability analysis to the Kundu–Mukherjee–Naskar model. Opt. Quant. Electron. 53, 283 (2021)

Bilal, M., Ur-Rehman, S., Ahmad, J.: Lump-periodic, some interaction phenomena and breather wave solutions to the (2+ 1)-r th dispersionless Dym equation. Mod. Phys. Lett. B 36(02), 2150547 (2022). https://doi.org/10.1142/S0217984921505473ADSMathSciNetCrossRef

Bilal, M., Rehman, S.U., Ahmad, J.: The study of new optical soliton solutions to the time-space fractional nonlinear dynamical model with novel mechanisms. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.05.027CrossRef

Bilal, M., Ur-Rehman, S., Ahmad, J.: Dynamics of diverse optical solitary wave solutions to the Biswas–Arshed equation in nonlinear optics. Int. J. Appl. Comput. Math. 8(3), 137 (2022)MathSciNetMATH

Biswas, A., Yildirim, Y., Yasar, E., Zhou, Q., Moshokoa, S.P., Belic, M.: Optical solitons for Lakshmanan–Porsezian–Daniel model by modified simple equation method. Optik 160, 24–32 (2018)ADS

Cheng, X., Hou, J., Wang, L.: Lie symmetry analysis, invariant subspace method and q-homotopy analysis method for solving fractional system of single-walled carbon nanotube. Comput. Appl. Math. 40(4), 1–17 (2021)MathSciNetMATH

Chukkol, Y. B., Mohamad, M. N., Muminov, M. I.: Exact solutions to the KDV-Burgers equation with forcing term using Tanh-Coth method. In AIP conference proceedings 1870, 040024, (2017)

El-Sayed, Z.E.S.M., Al-Nowehy, A.G.: Exact traveling wave solutions for nonlinear PDEs in mathematical physics using the generalized Kudryashov method. Serbian J. Electr. Eng. 13(2), 203–227 (2016)

El-Sheikh, M.M.A., Ahmed, H.M., Arnous, A.H., Rabie, W.B., Biswas, A., Alshomrani, A.S., Belic, M.R.: Optical solitons in birefringent fibers with Lakshmanan-Porsezian-Daniel model by modified simple equation. Optik 192, 162899 (2019)ADS

Fendzi-Donfack, E., Tala-Tebue, E., Inc, M., Kenfack-Jiotsa, A., Nguenang, J.P., Nana, L.: Dynamical behaviours and fractional alphabetical-exotic solitons in a coupled nonlinear electrical transmission lattice including wave obliqueness. Opt. Quant. Electron. 55(1), 35 (2023)

Guo, H.D., Xia, T.C., Tong, L.N.: Abundant solutions for the Lakshmanan–Porsezian–Daniel equation in an optical fiber through Riemann–Hilbert approach. Mod. Phys. Lett. B 36(21), 2250058 (2022). https://doi.org/10.1142/S0217984922500580ADSMathSciNetCrossRef

Hu, B.B., Lin, J., Zhang, L.: Dynamic behaviors of soliton solutions for a three-coupled Lakshmanan–Porsezian–Daniel model. Nonlinear Dyn. 107(3), 2773–2785 (2022)

Hubert, M.B., Betchewe, G., Justin, M., Doka, S.Y., Crepin, K.T., Biswas, A., Belic, M.: Optical solitons with Lakshmanan–Porsezian–Daniel model by modified extended direct algebraic method. Optik 162, 228–236 (2018)ADS

Hussain, S., Shah, A., Ullah, A., Haq, F.: The q-homotopy analysis method for a solution of the Cahn–Hilliard equation in the presence of advection and reaction terms. J. Taibah Univ. Sci. 16(1), 813–819 (2022)

Islam, Z., Abdeljabbar, A., Sheikh, M.A.N., Taher, M.A.: Optical solitons to the fractional order nonlinear complex model for wave packet envelope. Results Phys. 43, 106095 (2022)

Islam, S.R., Bashar, M.H., Arafat, S.Y., Wang, H., Roshid, M.M.: Effect of the free parameters on the Biswas–Arshed model with a unified technique. Chin. J. Phys. 77, 2501–2519 (2022)MathSciNet

Ismael, H.F., Akkilic, A.N., Murad, M.A.S., Bulut, H., Mahmoud, W., Osman, M.S.: Boiti–Leon–Manna–Pempinelli equation including time-dependent coefficient (vcBLMPE): a variety of nonautonomous geometrical structures of wave solutions. Nonlinear Dyn. 110(4), 3699–3712 (2022)

Jisha, C.R., Dubey, R.K.: Wave interactions and structures of (4+ 1)-dimensional Boiti–Leon–Manna–Pempinelli equation. Nonlinear Dyn. 110(4), 3685–3697 (2022)

Kumar, S., Mohan, B.: A novel and efficient method for obtaining Hirota’s bilinear form for the nonlinear evolution equation in (n+ 1) dimensions. Partial Differ. Equ. Appl. Math. 5, 100274 (2022)

Kumar, S., Malik, S., Rezazadeh, H., Akinyemi, L.: The integrable Boussinesq equation and it’s breather, lump and soliton solutions. Nonlinear Dyn. 107, 1–14 (2022)

Li, C., Chen, L., Li, G.: Optical solitons of space-time fractional Sasa–Satsuma equation by F-expansion method. Optik 224, 165527 (2020). https://doi.org/10.1016/j.ijleo.2020.165527ADSCrossRef

Liu, X., Zhang, H., Liu, W.: The dynamic characteristics of pure-quartic solitons and soliton molecules. Appl. Math. Model. 102, 305–312 (2022)MathSciNet

Malik, S., Kumar, S., Biswas, A., Yıldırım, Y., Moraru, L., Moldovanu, S., Alshehri, H.M.: Cubic-quartic optical solitons in fiber bragg gratings with dispersive reflectivity having parabolic law of nonlinear refractive index by lie symmetry. Symmetry 14(11), 2370 (2022)

Malik, S., Hashemi, M.S., Kumar, S., Rezazadeh, H., Mahmoud, W., Osman, M.S.: Application of new Kudryashov method to various nonlinear partial differential equations. Opt. Quant. Electron. 55(1), 8 (2023)

Manafian, J.: Variety interaction solutions comprising lump solitons for a generalized BK equation by trilinear analysis. Eur. Phys. J. Plus 136(10), 1–24 (2021)

Manafian, J., Foroutan, M., Guzali, A.: Applications of the ETEM for obtaining optical soliton solutions for the Lakshmanan–Porsezian–Daniel model. Eur. Phys. J. Plus 132, 1–22 (2017)

Mirhosseini-Alizamini, S.M., Rezazadeh, H., Eslami, M., Mirzazadeh, M., Korkmaz, A.: New extended direct algebraic method for the Tzitzica type evolution equations arising in nonlinear optics. Comput. Methods Differ. Equ. 8(1), 28–53 (2022)MATH

Modanli, M., Abdulazeez, S.T., Husien, A.M.: A residual power series method for solving pseudo hyperbolic partial differential equations with nonlocal conditions. Numer. Methods Partial Differ. Equ. 37(3), 2235–2243 (2021)MathSciNet

Mungkasi, S.: Variational iteration and successive approximation methods for a SIR epidemic model with constant vaccination strategy. Appl. Math. Model. 90, 1–10 (2021)MathSciNetMATH

Nadeem, M., He, J.H.: He-Laplace variational iteration method for solving the nonlinear equations arising in chemical kinetics and population dynamics. J. Math. Chem. 59(5), 1234–1245 (2021)MathSciNetMATH

Nestor, S., Justin, M., Douvagai, Betchewe, G., Doka, S.Y., Kofane, T.C.: New Jacobi elliptic solutions and other solutions with quadratic-cubic nonlinearity using two mathematical methods. Asian Eur. J. Math. 13(02), 2050043 (2020). https://doi.org/10.1142/S1793557120500436MathSciNetCrossRefMATH

Nestor, S., Betchewe, G., Inc, M., Doka, S.Y.: Exact traveling wave solutions to the higher-order nonlinear Schrödinger equation having Kerr nonlinearity form using two strategic integrations. Eur. Phys. J. Plus 135(4), 1–13 (2020)

Ng, R.T., Lakshmanan, L.V., Han, J., Pang, A.: Exploratory mining and pruning optimizations of constrained associations rules. ACM Sigmod Record 27(2), 13–24 (1998)

Noeiaghdam, S., Sidorov, D., Wazwaz, A.M., Sidorov, N., Sizikov, V.: The numerical validation of the adomian decomposition method for solving volterra integral equation with discontinuous kernels using the CESTAC method. Mathematics 9(3), 260 (2021)

Parker, A., Dye, J.M.: Boussinesq-type equations and switching solitons. Proc. Inst. Math. NAS Ukr. 43, 344–351 (2002)MathSciNetMATH

Qazza, A., Burqan, A., Saadeh, R.: Application of ARA-residual power series method in solving systems of fractional differential equations. Math. Probl. Eng. (2022). https://doi.org/10.1155/2022/6939045CrossRef

Rahman, R.U., Al-Maaitah, A.F., Qousini, M., Az-Zo’bi, E.A., Eldin, S.M., Abuzar, M.: New soliton solutions and modulation instability analysis of fractional Huxley equation. Results Phys. 44, 106163 (2023)

Rehman, S.U., Seadawy, A.R., Younis, M., Rizvi, S.T.R.: On study of modulation instability and optical soliton solutions: the chiral nonlinear Schrödinger dynamical equation. Opt. Quant. Electron. 52(8), 411 (2021)

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 (2022)

Rehman, S.U., Bilal, M., Inc, M., Younas, U., Rezazadeh, H., Younis, M., Mirhosseini-Alizamini, S.M.: Investigation of pure-cubic optical solitons in nonlinear optics. Opt. Quant. Electron. 54, 400 (2022)

Rezazadeh, H., Mirzazadeh, M., Mirhosseini-Alizamini, S.M., Neirameh, A., Eslami, M., Zhou, Q.: Optical solitons of Lakshmanan–Porsezian–Daniel model with a couple of nonlinearities. Optik 164, 414–423 (2018)ADS

Rezazadeh, H., Dhawan, S., Nestor, S., Bekir, A., Korkmaz, A.: Computational solutions of the generalized Ito equation in nonlinear dispersive systems. Int. J. Mod. Phys. B 35(13), 2150172 (2021). https://doi.org/10.1142/S0217979221501721ADSMathSciNetCrossRefMATH

Samir, I., Arnous, A.H., Yıldırım, Y., Biswas, A., Moraru, L., Moldovanu, S.: Optical solitons with cubic-quintic-septic-nonic nonlinearities and quadrupled power-law nonlinearity: an observation. Mathematics 10(21), 4085 (2022)

Savaissou, N., Gambo, B., Rezazadeh, H., Bekir, A., Doka, S.Y.: Exact optical solitons to the perturbed nonlinear Schrödinger equation with dual-power law of nonlinearity. Opt. Quant. Electron. 52, 1–16 (2020)

Sulaiman, T.A., Younas, U., Younis, M., Ahmad, J., Rehman, S.U., Bilal, M., Yusuf, A.: Modulation instability analysis, optical solitons and other solutions to the (2+ 1)-dimensional hyperbolic nonlinear Schrodinger’s equation. Comput. Methods Differ. Equ. 10(1), 179–190 (2022)MathSciNetMATH

Tanwar, D.V., Wazwaz, A.M.: Lie symmetries and exact solutions of KdV-Burgers equation with dissipation in dusty plasma. Qual. Theory Dyn. Syst. 21(4), 1–22 (2022)MathSciNetMATH

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). https://doi.org/10.1142/S0217984921505965MathSciNetCrossRef

Tariq, K.U., Wazwaz, A.M., Ahmed, A.: On some optical soliton structures to the Lakshmanan–Porsezian–Daniel model with a set of nonlinearities. Opt. Quant. Electron. 54(7), 432 (2022)

ur Rehman, S., Ahmad, J.: Modulation instability analysis and optical solitons in birefringent fibers to RKL equation without four wave mixing. Alex. Eng. J. 60(1), 1339–1354 (2021)

Wazwaz, A.M.: Partial differential equations and solitary waves theory. Springer, Berlin (2010)

Wazwaz, A.M., Alatawi, N.S., Albalawi, W., El-Tantawy, S.A.: Painlevé analysis for a new (3+ 1)-dimensional KP equation: multiple-soliton and lump solutions. Europhys. Lett. 140(5), 52002 (2022)

Yıldırım, Y., Topkara, E., Biswas, A., Triki, H., Ekici, M., Guggilla, P., Belic, M.R.: Cubic-quartic optical soliton perturbation with Lakshmanan–Porsezian–Daniel model by sine-Gordon equation approach. J. Opt. 50, 322–329 (2021)

Younas, U., Sulaiman, T.A., Ren, J.: On the study of optical soliton solutions to the three-component coupled nonlinear Schrödinger equation: applications in fiber optics. Opt. Quant. Electron. 55(1), 1–11 (2023)

Yusuf, A., Sulaiman, T.A., Alshomrani, A.S., Baleanu, D.: Breather and lump-periodic wave solutions to a system of nonlinear wave model arising in fluid mechanics. Nonlinear Dyn. 110(4), 3655–3669 (2022)

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, 1–15 (2022)

Zhao, X., Pang, F., Gegen, H.: Interactions among two-dimensional nonlinear localized waves and periodic wave solution for a novel integrable \((2+ 1)\)-dimensional KdV equation. Nonlinear Dyn. 110(4), 3629–3654 (2022)

Titel: Stability analysis and dynamical behavior of solitons in nonlinear optics modelled by Lakshmanan–Porsezian–Daniel equation
verfasst von: Sonia Akram
Jamshad Ahmad
Shafqat-Ur Rehman
Publikationsdatum: 01.08.2023
Verlag: Springer US
Erschienen in: Optical and Quantum Electronics / Ausgabe 8/2023
Print ISSN: 0306-8919
Elektronische ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-023-04986-4

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

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

Springer Professional "Technik"

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 8/2023

Deep learning based BER improvement for NOMA-VLC systems with perfect and imperfect successive interference cancellation

Spectral broadening in tight confinement geometry of a random fiber laser

Discussion on Peyrard Bishop DNA model for multi and breather waves, M-shaped rational and other interactional solutions

Non-classical correlations of accelerated observers interacting with a classical stochastic noise beyond the single mode approximation

Tailoring wide band gap PdS thin film doped with Cd ions using spin coating

Analytical solution for the dynamics and optimization of fractional Klein–Gordon equation: an application to quantum particle