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.
Similar content being viewed by others
Data availability
Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.
References
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.2022.07.002
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)
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)
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.2021.168356
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.2021.167987
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.2016.5.1
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/math10193456
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/s12043-015-1179-1
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.2022.02.012
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/10.1080/17455030.2022.2045044
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.2019.12.004
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)
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)
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)
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)
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)
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)
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)
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.2018.05.129
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)
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)
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)
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)
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)
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/S0217984919504013
Kudryashov, N.A.: Method for finding highly dispersive optical solitons of nonlinear differential equations. Optik 206, 163550 (2020)
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.2018.01.137
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/s11082-018-1383-6
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/s11082-019-1917-6
Liang, Z., Tang, X.: Painlevé analysis and exact solutions of the resonant Davey-Stewartson system. Phys. Lett. A 374(2), 110–115 (2009)
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)
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/s11082-022-03656-1
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-x
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)
Ozdemir, N.: Optical solitons for Radhakrishnan-Kundu-Lakshmanan equation in the presence of perturbation term and having kerr law. Optik 271, 170127 (2022)
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)
Ozisik, M., Bayram, M., Secer, A., Cinar, M.: Solitons in dual-core optical fibers with chromatic dispersion. Opt. Quantum Electron. 55(2), 162 (2023)
Ozisik, M., Secer, A., Bayram, M., Aydin, H.: An encyclopedia of kudryashov’s integrability approaches applicable to optoelectronic devices. Optik 265, 169499 (2022)
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)
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/10.1080/17455030.2018.1451009
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/s11082-019-1813-0
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-2021-0165
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/i2018-12027-9
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)
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)
Tang, X., Chow, K., Rogers, C.: Propagating wave patterns for the ‘Resonant’davey-Stewartson system. Chaos Solitons Fractals 42(5), 2707–2712 (2009)
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)
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)
Yıldırım, Y.: Optical solitons with biswas-arshed equation by f-expansion method. Optik 227, 165788 (2021)
Zedan, H.A., Monaquel, S.J.: The sine-cosine method for the davey-stewartson equations. Appl. Math. E-Notes 10, 103–111 (2010)
Zhao, Y.-M.: F-expansion method and its application for finding new exact solutions to the kudryashov-sinelshchikov equation. J. Appl. Math. (2013)
Funding
No funding for this article.
Author information
Authors and Affiliations
Contributions
All parts contained in the research were carried out by the authors through hard work and a review of the various references and contributions in the field of mathematics and Applied physics.
Corresponding author
Ethics declarations
Conflict of interest
This research received no specific grant from any funding agency in the public, commercial or not-for-profit sectors. The authors did not have any competing interests in this research.
Ethical approval
The Corresponding Author, declares that this manuscript is original, has not been published before, and is not currently being considered for publication elsewhere. The Corresponding Author confirms that the manuscript has been read and approved by all the named authors and there are no other persons who satisfied the criteria for authorship but are not listed. I further confirm that the order of authors listed in the manuscript has been approved by all of us. We understand that the Corresponding Author is the sole contact for the Editorial process and is responsible for communicating with the other authors about progress, submissions of revisions, and final approval of proofs.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Esen, H., Onder, I., Secer, A. et al. Davey-Stewartson system and investigation of the impacts of the nonlinearity. Opt Quant Electron 56, 246 (2024). https://doi.org/10.1007/s11082-023-05732-6
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s11082-023-05732-6