Top

Optical and Quantum Electronics

Published in:

01-02-2024

Davey-Stewartson system and investigation of the impacts of the nonlinearity

Authors: Handenur Esen, Ismail Onder, Aydin Secer, Muslum Ozisik, Mustafa Bayram

Published in: Optical and Quantum Electronics | Issue 2/2024

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

search-config

AI-assisted search

Off

Abstract

This study examines for the first time the adapted parabolic law nonlinearity form of (2+1)-dimensional Davey-Stewartson system, an important equation modeling the surface water wave packets with finite depth. For the first time, we will investigate the parabolic law nonlinearity form. Not only is this a significant aspect, but we will also explore it with various parameter values to see its impact on soliton dynamics. In order to transform the nonlinear partial differential equation into a form for which the analytical method can be applied, the ordinary differential equation structure obtained by first applying wave transformation. In the following stage, we implement the new Kudryashov method and sinh-Gordon equation expansion techniques to retrieve bright, dark, singular, and different types of kink solitons. The effect of parabolic law nonlinearity parameters on the obtained soliton types has also been examined. We illustrate the 3D and 2D graphs of some of the obtained solutions to gain a physical perspective. The study will contribute to the literature in terms of the form of the examined problem, its content and results, and the effectiveness of the applied methods.

previous article Optical -conformable normalized and recursional electroosmotic optimistic -conformable energy

next article Intelligent transportation system using wireless optical communication: a comparative study

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

Akbulut, A., Arnous, A.H., Hashemi, M.S., Mirzazadeh, M.: Solitary waves for the generalized nonlinear wave equation in (3+1) dimensions with gas bubbles using the Nnucci’s reduction, enhanced and modified Kudryashov algorithms. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.07.002CrossRef

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)CrossRefADS

Alabedalhadi, M., Al-Smadi, M., Al-Omari, S., Momani, S.: New optical soliton solutions for coupled resonant Davey-Stewartson system with conformable operator. Opt. Quantum Electron. 54(6), 392 (2022)CrossRef

Albayrak, P.: Optical solitons of biswas–milovic model having spatio-temporal dispersion and parabolic law via a couple of kudryashov’s schemes. Optik 170761 (2023)

Arnous, A.H.: Optical solitons to the cubic quartic Bragg gratings with anti-cubic nonlinearity using new approach. Optik (2022). https://doi.org/10.1016/j.ijleo.2021.168356CrossRef

Arnous, A.H.: Optical solitons with Biswas-Milovic equation in magneto-optic waveguide having Kudryashov’s law of refractive index. Optik 247, 167987 (2021). https://doi.org/10.1016/j.ijleo.2021.167987CrossRefADS

Arnous, A.H., Mirzazadeh, M.: Application of the generalized Kudryashov method to the Eckhaus equation. Nonlinear Anal. Modell. Control. 21(5), 577–586 (2016). https://doi.org/10.15388/NA.2016.5.1MathSciNetCrossRef

Arnous, A.H., Moraru, L.: Optical solitons with the complex Ginzburg-Landau equation with Kudryashov’s law of refractive index. Mathematics 10(19), 3456 (2022). https://doi.org/10.3390/math10193456CrossRef

Arnous, A.H., Mirzazadeh, M., Eslami, M.: Exact solutions of the Drinfel’d-Sokolov-Wilson equation using Bäcklund transformation of Riccati equation and trial function approach. Pramana J. Phys. 86(6), 1153–1160 (2016). https://doi.org/10.1007/s12043-015-1179-1CrossRefADS

Arnous, A.H., Mirzazadeh, M., Akinyemi, L., Akbulut, A.: New solitary waves and exact solutions for the fifth-order nonlinear wave equation using two integration techniques. J. Ocean Eng. Sci. (2022). https://doi.org/10.1016/j.joes.2022.02.012CrossRef

Arnous, A.H., Mirzazadeh, M., Akbulut, A., Akinyemi, L.: Optical solutions and conservation laws of the Chen-Lee-Liu equation with Kudryashov’s refractive index via two integrable techniques. Waves Random Complex Media (2022). https://doi.org/10.1080/17455030.2022.2045044CrossRef

Arshed, S., Raza, N.: Optical solitons perturbation of Fokas-Lenells equation with full nonlinearity and dual dispersion. Chin. J. Phys. 63, 314–324 (2020). https://doi.org/10.1016/j.cjph.2019.12.004MathSciNetCrossRef

Arshed, S., Raza, N., Alansari, M.: Soliton solutions of the generalized Davey-Stewartson equation with full nonlinearities via three integrating schemes. Ain Shams Eng. J. 12(3), 3091–3098 (2021)CrossRef

Cakicioglu, H., Ozisik, M., Secer, A., Bayram, M.: Stochastic dispersive schrödinger-hirota equation having parabolic law nonlinearity with multiplicative white noise via ito calculus. Optik 279, 170776 (2023)CrossRefADS

Davey, A., Stewartson, K.: Stewartson on three-dimensional packets of surface waves, proceedings of the royal society of London. A Math. Phys. Sci. 338(1613), 101–110 (1974)

Debnath, L.: Nonlinear water waves, (1994)

Ebadi, G., Krishnan, E., Labidi, M., Zerrad, E., Biswas, A.: Analytical and numerical solutions to the Davey-Stewartson equation with power-law nonlinearity. Waves Random Complex Med. 21(4), 559–590 (2011)MathSciNetCrossRefADS

Ebaid, A., Aly, E.H.: Exact solutions for the transformed reduced ostrovsky equation via the f-expansion method in terms of weierstrass-elliptic and jacobian-elliptic functions. Wave Motion 49(2), 296–308 (2012)MathSciNetCrossRefADS

El-Shiekh, R.M., Gaballah, M.: Solitary wave solutions for the variable-coefficient coupled nonlinear schrödinger equations and davey-stewartson system using modified sine-gordon equation method. J. Ocean Eng. Sci. 5(2), 180–185 (2020)CrossRef

El-Shiekh, R.M., Gaballah, M.: Novel solitons and periodic wave solutions for Davey-Stewartson system with variable coefficients. J. Taibah Univ. Sci. 14(1), 783–789 (2020)CrossRef

Esen, H., Secer, A., Ozisik, M., Bayram, M.: Analytical soliton solutions of the higher order cubic-quintic nonlinear schrödinger equation and the influence of the model’s parameters. J. Appl. Phys. 132(5), 053103 (2022)CrossRefADS

Foroutan, M., Kumar, D., Manafian, J., Hoque, A.: New explicit soliton and other solutions for the conformable fractional Biswas-Milovic equation with Kerr and parabolic nonlinearity through an integration scheme. Optik 170, 190–202 (2018). https://doi.org/10.1016/j.ijleo.2018.05.129CrossRefADS

Gaballah, M., El-Shiekh, R. M., Akinyemi, L., Rezazadeh, H.: Novel periodic and optical soliton solutions for davey–stewartson system by generalized jacobi elliptic expansion method. Int. J. Nonlinear Sci. Numer. Simul. (2022)

Guo, J., He, J., Li, M., Mihalache, D.: Exact solutions with elastic interactions for the (2+ 1)-dimensional extended Kadomtsev-Petviashvili equation. Nonlinear Dyn. 101(4), 2413–2422 (2020)CrossRef

Guo, L., Kevrekidis, P.G., He, J.: Asymptotic dynamics of higher-order lumps in the Davey-Stewartson II equation. J. Phys. A Math. Theor. 55(47), 475701 (2022)MathSciNetCrossRefADS

Hereman, W., Zhuang, W.: Symbolic Computation of Solitons via Hirota’s Bilinear Method. Department of Mathematical and Computer Sciences, Colorado, School of Mines (1994)

Ismael, H.F., Atas, S.S., Bulut, H., Osman, M.: Analytical solutions to the m-derivative resonant Davey-Stewartson equations. Modern Phys. Lett. B 35(30), 2150455 (2021)MathSciNetCrossRefADS

Ismael, H.F., Sulaiman, T.A., Yusuf, A., Bulut, H.: Resonant Davey-Stewartson system: dark, bright mixed dark-bright optical and other soliton solutions. Opt. Quantum Electron. 55(1), 48 (2023)CrossRef

Jafari, H., Sooraki, A., Talebi, Y., Biswas, A.: The first integral method and traveling wave solutions to Davey-Stewartson equation. Nonlinear Anal. Modell. Control 17(2), 182–193 (2012)MathSciNetCrossRef

Javid, A., Raza, N.: Chiral solitons of the (1 + 2)-dimensional nonlinear Schrodinger’s equation. Modern Phys. Lett. B (2019). https://doi.org/10.1142/S0217984919504013MathSciNetCrossRef

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

Kumar, D., Manafian, J., Hawlader, F., Ranjbaran, A.: New closed form soliton and other solutions of the Kundu-Eckhaus equation via the extended Sinh-Gordon equation expansion method. Optik 160, 159–167 (2018). https://doi.org/10.1016/j.ijleo.2018.01.137CrossRefADS

Kumar, D., Seadawy, A.R., Chowdhury, R.: On new complex soliton structures of the nonlinear partial differential equation describing the pulse narrowing nonlinear transmission lines. Opt. Quantum Electron. 50(2), 1–14 (2018). https://doi.org/10.1007/s11082-018-1383-6CrossRef

Kumar, D., Joardar, A.K., Hoque, A., Paul, G.C.: Investigation of dynamics of nematicons in liquid crystals by extended sinh-Gordon equation expansion method. Opt. Quantum Electron. 51(7), 1–36 (2019). https://doi.org/10.1007/s11082-019-1917-6CrossRef

Liang, Z., Tang, X.: Painlevé analysis and exact solutions of the resonant Davey-Stewartson system. Phys. Lett. A 374(2), 110–115 (2009)MathSciNetCrossRefADS

Li, B., Ye, W.-C., Chen, Y.: Symmetry, full symmetry groups, and some exact solutions to a generalized Davey-Stewartson system. J. Math. Phys. 49(10), 103503 (2008)MathSciNetCrossRefADS

Mathanaranjan, T., Kumar, D., Rezazadeh, H., Akinyemi, L.: Optical solitons in metamaterials with third and fourth order dispersions. Opt. Quantum Electron. 54(5), 1–15 (2022). https://doi.org/10.1007/s11082-022-03656-1CrossRef

Mirzazadeh, M., Eslami, M., Arnous, A.H.: Dark optical solitons of Biswas-Milovic equation with dual-power law nonlinearity. Eur. Phys. J. Plus 130(1), 1–7 (2015). https://doi.org/10.1140/epjp/i2015-15004-xCrossRef

Onder, I., Secer, A., Ozisik, M., Bayram, M.: Obtaining optical soliton solutions of the cubic-quartic Fokas-Lenells equation via three different analytical methods. Opt. Quantum Electron. 54(12), 786 (2022)CrossRef

Ozdemir, N.: Optical solitons for Radhakrishnan-Kundu-Lakshmanan equation in the presence of perturbation term and having kerr law. Optik 271, 170127 (2022)CrossRefADS

Ozisik, M.: Novel (2+ 1) and (3+ 1) forms of the Biswas-Milovic equation and optical soliton solutions via two efficient techniques. Optik 269, 169798 (2022)CrossRefADS

Ozisik, M., Bayram, M., Secer, A., Cinar, M.: Solitons in dual-core optical fibers with chromatic dispersion. Opt. Quantum Electron. 55(2), 162 (2023)CrossRef

Ozisik, M., Secer, A., Bayram, M., Aydin, H.: An encyclopedia of kudryashov’s integrability approaches applicable to optoelectronic devices. Optik 265, 169499 (2022)CrossRefADS

Ozisik, M., Onder, I., Esen, H., Cinar, M., Ozdemir, N., Secer, A., Bayram, M.: On the investigation of optical soliton solutions of cubic-quartic Fokas-Lenells and schrödinger-Hirota equations. Optik 272, 170389 (2023)CrossRefADS

Peregrine, D.H.: Water waves, nonlinear schrödinger equations and their solutions. ANZIAM J. 25(1), 16–43 (1983)

Raza, N., Javid, A.: Optical dark and dark-singular soliton solutions of (1+2)-dimensional chiral nonlinear Schrodinger’s equation. Waves Random Complex Med. 29(3), 496–508 (2019). https://doi.org/10.1080/17455030.2018.1451009MathSciNetCrossRefADS

Raza, N., Afzal, U., Butt, A.R., Rezazadeh, H.: Optical solitons in nematic liquid crystals with Kerr and parabolic law nonlinearities. Opt. Quantum Electron. 51(4), 1–16 (2019). https://doi.org/10.1007/s11082-019-1813-0CrossRef

Raza, N., Javid, A., Butt, A.R., Baskonus, H.M.: Optical solitons and stability regions of the higher order nonlinear Schrödinger’s equation in an inhomogeneous fiber. Int. J. Nonlinear Sci. Numer. Simul. 24(2), 567–579 (2023). https://doi.org/10.1515/ijnsns-2021-0165MathSciNetCrossRef

Satsuma, J.: Hirota bilinear method for nonlinear evolution equations. In: Direct and Inverse Methods in Nonlinear Evolution Equations: Lectures Given at the CIME Summer School Held in Cetraro, Italy, September 5-12, 1999, Springer, pp. 171–222 (2003)

Seadawy, A.R., Kumar, D., Chakrabarty, A.K.: Dispersive optical soliton solutions for the hyperbolic and cubic-quintic nonlinear Schrödinger equations via the extended sinh-Gordon equation expansion method. Eur. Phys. J. Plus 133(5), 1–11 (2018). https://doi.org/10.1140/epjp/i2018-12027-9CrossRef

Selima, E.S., Seadawy, A.R., Yao, X.: The nonlinear dispersive davey-stewartson system for surface waves propagation in shallow water and its stability. Eur. Phys. J. Plus 131, 1–16 (2016)CrossRef

Shahoot, A., Alurrfi, K., Hassan, I., Almsri, A.: Solitons and other exact solutions for two nonlinear pdes in mathematical physics using the generalized projective riccati equations method. Adv. Math. Phys. (2018)

Sun, Y., Tian, B., Yuan, Y.-Q., Du, Z.: Semi-rational solutions for a \((2+ 1)-\)dimensional davey-stewartson system on the surface water waves of finite depth. Nonlinear Dyn. 94, 3029–3040 (2018)CrossRef

Tang, X., Chow, K., Rogers, C.: Propagating wave patterns for the ‘Resonant’davey-Stewartson system. Chaos Solitons Fractals 42(5), 2707–2712 (2009)CrossRefADS

Whitham, G. B.: Linear and nonlinear waves. Wiley (2011)

Yan, Z.: Jacobi elliptic function solutions of nonlinear wave equations via the new Sinh-Gordon equation expansion method. J. Phys. A Math. General 36(7), 1961 (2003)MathSciNetCrossRefADS

Yan, Z.: A sinh-gordon equation expansion method to construct doubly periodic solutions for nonlinear differential equations. Chaos Solitons Fractals 16(2), 291–297 (2003)MathSciNetCrossRefADS

Yıldırım, Y.: Optical solitons with biswas-arshed equation by f-expansion method. Optik 227, 165788 (2021)CrossRefADS

Zedan, H.A., Monaquel, S.J.: The sine-cosine method for the davey-stewartson equations. Appl. Math. E-Notes 10, 103–111 (2010)MathSciNet

Zhao, Y.-M.: F-expansion method and its application for finding new exact solutions to the kudryashov-sinelshchikov equation. J. Appl. Math. (2013)

Title: Davey-Stewartson system and investigation of the impacts of the nonlinearity
Authors: Handenur Esen
Ismail Onder
Aydin Secer
Muslum Ozisik
Mustafa Bayram
Publication date: 01-02-2024
Publisher: Springer US
Published in: Optical and Quantum Electronics / Issue 2/2024
Print ISSN: 0306-8919
Electronic ISSN: 1572-817X
DOI: https://doi.org/10.1007/s11082-023-05732-6

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 2/2024

Simulation of optical image enhancement algorithm based on reinforcement learning in evaluating the quality of physical education teaching for college students

Effects of irradiation time on the structural, elastic, and optical properties of hexagonal (wurtzite) zinc oxide nanoparticle synthesised via microwave-assisted hydrothermal route

Application of light imaging detection based on data information visualization in aerobics training management competition simulation system

Evaluation of infrared image detection based on HOG feature extraction in swimmer training effectiveness

Performance analysis of 3 × 10 Gb/s UOWC transmission system based on OCDMA using a DPS code

Optical fiber dual-parameter sensors based on different kinds of interferometers for measuring refractive index and temperature: a review