{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,8]],"date-time":"2026-06-08T10:53:24Z","timestamp":1780916004955,"version":"3.54.1"},"reference-count":45,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,10,17]],"date-time":"2022-10-17T00:00:00Z","timestamp":1665964800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, the stochastic Davey\u2013Stewartson equations (SDSEs) forced by multiplicative noise are addressed. We use the mapping method to find new rational, elliptic, hyperbolic and trigonometric functions. In addition, we generalize some previously obtained results. Due to the significance of the Davey\u2013Stewartson equations in plasma physics, nonlinear optics, hydrodynamics and other fields, the discovered solutions are useful in explaining a number of intriguing physical phenomena. By using MATLAB tools to simulate our results and display some of 3D graphs, we show how the multiplicative Brownian motion impacts the analytical solutions of the SDSEs. Finally, we demonstrate the effect of multiplicative Brownian motion on the stability and the symmetry of the achieved solutions of the SDSEs.<\/jats:p>","DOI":"10.3390\/sym14102176","type":"journal-article","created":{"date-parts":[[2022,10,17]],"date-time":"2022-10-17T05:08:02Z","timestamp":1665983282000},"page":"2176","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":46,"title":["Multiplicative Brownian Motion Stabilizes the Exact Stochastic Solutions of the Davey\u2013Stewartson Equations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2394-0041","authenticated-orcid":false,"given":"Farah M.","family":"Al-Askar","sequence":"first","affiliation":[{"name":"Department of Mathematical Science, Collage of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1694-7907","authenticated-orcid":false,"given":"Clemente","family":"Cesarano","sequence":"additional","affiliation":[{"name":"Section of Mathematics, International Telematic University Uninettuno, Corso, Vittorio Emanuele II, 39, 00186 Roma, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1402-7584","authenticated-orcid":false,"given":"Wael W.","family":"Mohammed","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Collage of Science, University of Ha\u2019il, Ha\u2019il 2440, Saudi Arabia"},{"name":"Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,17]]},"reference":[{"key":"ref_1","first-page":"1196","article-title":"The tanh method: Exact solutions of the Sine\u2013Gordon and Sinh\u2013Gordon equations","volume":"167","author":"Wazwaz","year":"2005","journal-title":"Appl. Math. Comput."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Mohammed, W.W., Alshammari, M., Cesarano, C., and El-Morshedy, M. (2022). Brownian Motion Effects on the Stabilization of Stochastic Solutions to Fractional Diffusion Equations with Polynomials. Mathematics, 10.","DOI":"10.3390\/math10091458"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Al-Askar, E.M., Mohammed, W.W., Albalahi, A.M., and El-Morshedy, M. (2022). The Impact of the Wiener process on the analytical solutions of the stochastic (2+1)-dimensional breaking soliton equation by using tanh\u2013coth method. Mathematics, 10.","DOI":"10.3390\/math10050817"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"11947","DOI":"10.1016\/j.aej.2022.05.046","article-title":"Analytical behavior of soliton solutions to the couple type fractional-order nonlinear evolution equations utilizing a novel technique","volume":"61","author":"Zaman","year":"2022","journal-title":"Alex. Eng. J."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"9949","DOI":"10.1016\/j.aej.2022.03.033","article-title":"New dynamical soliton propagation of fractional type couple modified equal-width and Boussinesq equations","volume":"61","author":"Khatun","year":"2022","journal-title":"Alex. Eng. J."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1016\/S0378-4754(02)00255-0","article-title":"An analytic study of compactons structures in a class of nonlinear dispersive equations","volume":"63","author":"Wazwaz","year":"2003","journal-title":"Math. Comput. Simul."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1007\/s13324-021-00477-5","article-title":"A binary darboux transformation for multicomponent NLS equations and their reductions","volume":"11","author":"Sumayah","year":"2021","journal-title":"Anal. Math. Phys."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"299","DOI":"10.1016\/S0960-0779(02)00653-7","article-title":"Abunbant families of Jacobi elliptic function solutions of the-dimensional integrable Davey-Stewartson-type equation via a new method","volume":"18","author":"Yan","year":"2003","journal-title":"Chaos Solitons Fract."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/S0375-9601(02)01516-5","article-title":"Applications of the Jacobi elliptic function method to special-type nonlinear equations","volume":"305","author":"Fan","year":"2002","journal-title":"Phys. Lett. A"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"499","DOI":"10.1016\/j.mcm.2003.12.010","article-title":"A sine-cosine method for handling nonlinear wave equations","volume":"40","author":"Wazwaz","year":"2004","journal-title":"Math. Comput. Model."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/S0375-9601(96)00770-0","article-title":"A simple transformation for nonlinear waves","volume":"224","author":"Yan","year":"1996","journal-title":"Phys. Lett. A"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1016\/j.physleta.2007.07.051","article-title":"The (G\u2019\/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics","volume":"372","author":"Wang","year":"2008","journal-title":"Phys. Lett. A"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3220","DOI":"10.1016\/j.cnsns.2009.01.006","article-title":"New application of the (G\u2019\/G)-expansion method","volume":"14","author":"Zhang","year":"2009","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1192","DOI":"10.1103\/PhysRevLett.27.1192","article-title":"Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons","volume":"27","author":"Hirota","year":"1971","journal-title":"Phys. Rev. Lett."},{"key":"ref_15","first-page":"72","article-title":"The exp(\u2212(\u03c2))-expansion method for finding travelling wave solutions of Vakhnenko-Parkes equation","volume":"5","author":"Khan","year":"2014","journal-title":"Int. J. Dyn. Syst. Differ. Equ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"961","DOI":"10.1080\/07362994.2016.1197131","article-title":"Fast-Diffusion Limit with Large Noise for Systems of Stochastic Reaction-Diffusion Equations","volume":"34","author":"Mohammed","year":"2016","journal-title":"Stoch. Anal. Appl."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"124808","DOI":"10.1016\/j.jmaa.2020.124808","article-title":"Fast-diffusion limit for reaction-diffusion equations with multiplicative noise","volume":"496","author":"Mohammed","year":"2021","journal-title":"J. Math. Anal. Appl."},{"key":"ref_18","first-page":"955","article-title":"Dynamical behaviour of nondissipative double dispersive microstrain wave in the microstructured solids","volume":"136","author":"Elbrolosy","year":"2021","journal-title":"Eur. Phys. J."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1080\/16583655.2019.1709271","article-title":"Bifurcation and travelling wave solutions for a (2+1)-dimensional KdV equation","volume":"14","author":"Elmandouha","year":"2020","journal-title":"J. Taibah Univ. Sci."},{"key":"ref_20","first-page":"1","article-title":"Bifurcation and new traveling wave solutions for the 2D Ginzburg\u2013Landau equation","volume":"135","author":"Elmandouha","year":"2020","journal-title":"Eur. Phys. Plus"},{"key":"ref_21","first-page":"533","article-title":"Construction of new traveling wave solutions for the (2+1) dimensional extended kadomtsev-petviashvili equation","volume":"12","author":"Elbrolosy","year":"2022","journal-title":"J. Appl. Anal. Comput."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Elmandouh, A.A., and Elbrolosy, M.E. (2022). New traveling wave solutions for Gilson\u2013Pickering equation in plasma via bifurcation analysis and direct method. Math. Methods Appl. Sci., accepted.","DOI":"10.1002\/mma.8506"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"117","DOI":"10.1186\/s13662-015-0452-4","article-title":"A Riccati-Bernoulli sub-ODE method for nonlinear partial differential equations and its application","volume":"1","author":"Yang","year":"2015","journal-title":"Adv. Diff. Equa."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"14","DOI":"10.1155\/2014\/534063","article-title":"Sonmezoglu A. F-expansion method and new exact solutions of the Schr\u00f6dinger-KdV equation","volume":"2014","author":"Filiz","year":"2014","journal-title":"Sci. World J."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Arnold, L. (1998). Random Dynamical Systems, Springer.","DOI":"10.1007\/978-3-662-12878-7"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/978-3-642-18756-8_1","article-title":"Some recent progress in multiscale modeling","volume":"Volume 39","author":"Weinan","year":"2004","journal-title":"Multiscale Modeling and Simulation"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1186\/s13662-016-0814-6","article-title":"Amplitude equation with quintic nonlinearities for the generalized Swift-Hohenberg equation with additive degenerate noise","volume":"2016","author":"Mohammed","year":"2016","journal-title":"Adv. Differ. Equ."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Mohammed, W.W., Iqbal, N., and Botmart, T. (2020). Additive noise effects on the stabilization of fractional-space diffusion equation solutions. Mathematics, 10.","DOI":"10.3390\/math10010130"},{"key":"ref_29","unstructured":"Kloeden, P.E., and Platen, E. (1995). Numerical Solution of Stochastic Differential Equations, Springer."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"101","DOI":"10.1098\/rspa.1974.0076","article-title":"On three-dimensional packets of surface waves","volume":"338","author":"Davey","year":"1974","journal-title":"Proc. Royal. Soc. Lond. Ser. A"},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"915","DOI":"10.1016\/j.cnsns.2012.08.034","article-title":"Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi\u2019s elliptic function method","volume":"18","author":"Bhrawy","year":"2013","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"182","DOI":"10.15388\/NA.17.2.14067","article-title":"The first integral method and traveling wave solutions to Davey\u2013Stewartson equation","volume":"17","author":"Jafari","year":"2012","journal-title":"Nonlinear Anal. Model. Control"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"1775","DOI":"10.1007\/s11071-015-2276-x","article-title":"Soliton solutions of Davey\u2013Stewartson equation by trial equation method and ansatz approach","volume":"82","author":"Mirzazadeh","year":"2015","journal-title":"Nonlinear Dyn."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"227","DOI":"10.1007\/s42791-019-00025-0","article-title":"Constructing new wave solutions to the (2+1)-dimensional Davey\u2013Stewartson equation (DSE) which arises in fluid dynamics","volume":"1","year":"2019","journal-title":"JMST Adv."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1515\/IJNSNS.2009.10.7.927","article-title":"Double exp-function method and application","volume":"10","author":"Fu","year":"2009","journal-title":"Int. J. Nonlinear Sci. Numer. Simul."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"91","DOI":"10.5539\/jmr.v6n2p91","article-title":"Exact Solutions for the nonlinear (2+1)-dimensional Davey-Stewartson equation using the generalized (G\u2019\/G)-expansion method","volume":"6","author":"Abdelaziz","year":"2014","journal-title":"J. Math. Res."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"694","DOI":"10.1016\/j.mcm.2010.10.005","article-title":"The (G\u2019\/G) method and 1-soliton solution of the Davey\u2013Stewartson equation","volume":"53","author":"Ebadi","year":"2011","journal-title":"Math. Comput. Model."},{"key":"ref_38","first-page":"103","article-title":"The sine-cosine method for the Davey-Stewartson equations","volume":"10","author":"Zedan","year":"2010","journal-title":"Appl. Math. E-Notes"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"401","DOI":"10.1016\/S0375-9601(03)00909-5","article-title":"Exact solutions for some nonlinear partial differential equations","volume":"314","author":"Peng","year":"2003","journal-title":"Phys. Lett. A"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1375","DOI":"10.3934\/cpaa.2008.7.1375","article-title":"Stabilisation of differential inclusions and PDEs without uniqueness by noise","volume":"7","author":"Caraballo","year":"2008","journal-title":"Commun. Pure Appl. Anal."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1016\/j.sysconle.2004.02.020","article-title":"Stabilisation of linear PDEs by Stratonovich noise","volume":"53","author":"Caraballo","year":"2004","journal-title":"Syst. Control. Lett."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"735","DOI":"10.1007\/BF01025992","article-title":"Noise-induced global asymptotic stability","volume":"60","author":"Mackey","year":"1990","journal-title":"J. Stat. Phys."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"3905","DOI":"10.1088\/1361-6544\/ab801e","article-title":"The impact of multiplicative noise in SPDEs close to bifurcation via amplitude equations","volume":"33","author":"Fu","year":"2020","journal-title":"Nonlinearity"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1142\/9789814277266_0003","article-title":"Stabilization of evolution equations by noise","volume":"8","author":"Caraballo","year":"2009","journal-title":"Interdiscip. Math. Sci."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"525","DOI":"10.1137\/S0036144500378302","article-title":"An algorithmic introduction to numerical simulation of stochastic differential equations","volume":"43","author":"Higham","year":"2001","journal-title":"SIAM Rev."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2176\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T00:55:32Z","timestamp":1760144132000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/14\/10\/2176"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,10,17]]},"references-count":45,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2022,10]]}},"alternative-id":["sym14102176"],"URL":"https:\/\/doi.org\/10.3390\/sym14102176","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,10,17]]}}}