{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T22:56:53Z","timestamp":1773097013129,"version":"3.50.1"},"reference-count":36,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T00:00:00Z","timestamp":1760400000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this paper, we investigate the generalized coupled Zakharov system (GCZS), a fundamental model in plasma physics that describes the nonlinear interaction between high-frequency Langmuir waves and low-frequency ion-acoustic waves, including the influence of magnetic fields on weak ion-acoustic wave propagation. This research aims to achieve three main objectives. First, we uncover soliton solutions of the coupled system in hyperbolic, trigonometric, and rational forms, both in single and combined expressions. These results are obtained using the extended rational sinh-Gordon expansion method and the G\u2032G,1G-expansion method. Second, we analyze the dynamic characteristics of the model by performing bifurcation and sensitivity analyses and identifying the corresponding Hamiltonian function. To understand the mechanisms of intricate physical phenomena and dynamical processes, we plot 2D, 3D, and contour diagrams for appropriate parameter values. We also analyze the bifurcation of phase portraits of the ordinary differential equations corresponding to the investigated partial differential equation. The novelty of this study lies in the fact that the proposed model has not been previously explored using these advanced methods and comprehensive dynamical analyses.<\/jats:p>","DOI":"10.3390\/axioms14100763","type":"journal-article","created":{"date-parts":[[2025,10,15]],"date-time":"2025-10-15T11:57:42Z","timestamp":1760529462000},"page":"763","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Dispersive Soliton Solutions and Dynamical Analyses of a Nonlinear Model in Plasma Physics"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0465-7299","authenticated-orcid":false,"given":"Alwaleed","family":"Kamel","sequence":"first","affiliation":[{"name":"Department of Mathematics, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0003-6122-0779","authenticated-orcid":false,"given":"Ali H.","family":"Tedjani","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7767-9785","authenticated-orcid":false,"given":"Shafqat Ur","family":"Rehman","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Grand Asian University, Sialkot 51310, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Muhammad","family":"Bilal","sequence":"additional","affiliation":[{"name":"Department of Physics, Shanghai University, Shanghai 200444, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Alawia","family":"Adam","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, Buraydah 51452, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5731-3532","authenticated-orcid":false,"given":"Khaled","family":"Aldwoah","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Islamic University of Madinah, Madinah 42351, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0005-2954-1753","authenticated-orcid":false,"given":"Mohammed","family":"Messaoudi","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 11564, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2025,10,14]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"085230","DOI":"10.1088\/1402-4896\/ad5fcd","article-title":"Soliton solutions and sensitive analysis to nonlinear wave model arising in optics","volume":"99","author":"Lu","year":"2024","journal-title":"Phys. Scr."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2450075","DOI":"10.1142\/S0217979224500759","article-title":"A variety of soliton solutions of the extended Gerdjikov\u2013Ivanov equation in the DWDM system","volume":"38","author":"Raza","year":"2024","journal-title":"Int. J. Mod. Phys. B"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"103510","DOI":"10.1016\/j.asej.2025.103510","article-title":"On the study of multiple wave profiles and hybrid phenomena to the newly developed multi-component Gross-Pitaevskii system and stability analysis","volume":"16","author":"Bilal","year":"2025","journal-title":"Ain Shams Eng. J."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Pleumpreedaporn, C., Moore, E.J., Sirisubtawee, S., Khansai, N., and Pleumpreedaporn, S. (2024). Exact Solutions for the Sharma\u2013Tasso\u2013Olver Equation via the Sardar Subequation Method with a Comparison between Atangana Space\u2013Time Beta-Derivatives and Classical Derivatives. Mathematics, 12.","DOI":"10.3390\/math12142155"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.1007\/s12596-024-01812-2","article-title":"Soliton patterns in the truncated M-fractional resonant nonlinear Schr\u00f6dinger equation via modified Sardar sub-equation method","volume":"54","author":"Ahmad","year":"2024","journal-title":"J. Opt."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"1294","DOI":"10.1007\/s11082-024-07015-0","article-title":"Modulation instability and optical wave profiles for the conformable Schr\u00f6dinger\u2013Poisson dynamical system","volume":"56","author":"Yasin","year":"2024","journal-title":"Opt. Quantum Electron."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"640","DOI":"10.1007\/s11082-022-03961-9","article-title":"Dynamics of optical and multiple lump solutions to the fractional coupled nonlinear Schr\u00f6dinger equation","volume":"54","author":"Rehman","year":"2022","journal-title":"Opt. Quantum Electron."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s11082-023-05587-x","article-title":"Dynamics of nonlinear diverse wave propagation to Improved Boussinesq model in weakly dispersive medium of shallow waters or ion acoustic waves using efficient technique","volume":"56","author":"Bilal","year":"2024","journal-title":"Opt. Quantum Electron."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Ali, A., Ahmad, J., Javed, S., Hussain, R., and Alaoui, M.K. (2024). Numerical simulation and investigation of soliton solutions and chaotic behavior to a stochastic nonlinear Schr\u00f6dinger model with a random potential. PLoS ONE, 19.","DOI":"10.1371\/journal.pone.0296678"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"98","DOI":"10.1007\/s13538-024-01468-0","article-title":"Analysis of Dust-Ion Acoustic Soliton and ShockWaves of Damped KdV Burgers\u2019 Equation in Superthermal Plasmas: Adomian Decomposition Approach","volume":"54","author":"Kumar","year":"2024","journal-title":"Braz. J. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"107556","DOI":"10.1016\/j.rinp.2024.107556","article-title":"Construction of optical solitary wave solutions and their propagation for Kuralay system using tanh\u2014Coth and energy balance method","volume":"59","author":"Ali","year":"2024","journal-title":"Results Phys."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2450380","DOI":"10.1142\/S0217984924503809","article-title":"On the investigation of fractional coupled nonlinear integrable dynamical system: Dynamics of soliton solutions","volume":"38","author":"Muhammad","year":"2024","journal-title":"Mod. Phys. Lett. B"},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"106719","DOI":"10.1016\/j.rinp.2023.106719","article-title":"Description of soliton and lump solutions to M-truncated stochastic Biswas\u2013Arshed model in optical communication","volume":"51","author":"Ahmad","year":"2023","journal-title":"Results Phys."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"106171","DOI":"10.1016\/j.rinp.2022.106171","article-title":"Applications of two novel techniques in finding optical soliton solutions of modified nonlinear Schr\u00f6dinger equations","volume":"44","author":"Ghanbari","year":"2023","journal-title":"Results Phys."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1140\/epjp\/s13360-024-05205-z","article-title":"Deformation of inhomogeneous vector optical rogue waves in the variable coefficients coupled cubic\u2013quintic nonlinear Schr\u00f6dinger equations with self-steepening","volume":"139","author":"Manigandan","year":"2024","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Kirci, O., Pand\u0131r, Y., and Bulut, H. (2024). Different wave structures in water wave mechanics with two conformable models. J. Appl. Math. Comput., 71.","DOI":"10.1007\/s12190-024-02222-0"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2611","DOI":"10.1007\/s11071-024-10320-8","article-title":"Stability analysis and solitary wave solutions for Yu Toda Sasa Fukuyama equation","volume":"113","author":"Rizvi","year":"2025","journal-title":"Nonlinear Dyn."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"3480","DOI":"10.1002\/mma.8726","article-title":"Extraction of the gravitational potential and high frequency wave perturbation properties of nonlinear (3+1)-dimensional Vakhnenko\u2013Parkes equation via novel approach","volume":"47","author":"Yan","year":"2024","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"105590","DOI":"10.1016\/j.rineng.2025.105590","article-title":"Soliton Solutions and Wave Dynamics of Complex Fractional Models in Nonlinear Optics","volume":"26","author":"Akbar","year":"2025","journal-title":"Results Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1140\/epjp\/s13360-024-05435-1","article-title":"The study of phase portraits, multistability visualization, Lyapunov exponents and chaos identification of coupled nonlinear volatility and option pricing model","volume":"139","author":"Jhangeer","year":"2024","journal-title":"Eur. Phys. J. Plus"},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Li, Z., Lyu, J., and Hussain, E. (2024). Bifurcation, chaotic behaviors and solitary wave solutions for the fractional Twin-Core couplers with Kerr law non-linearity. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-74044-w"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"075217","DOI":"10.1088\/1402-4896\/acdcee","article-title":"Analysis of chaotic structures, bifurcation and soliton solutions to fractional Boussinesq model","volume":"98","author":"Ali","year":"2023","journal-title":"Phys. Scr."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1007\/s40819-021-01217-w","article-title":"New optical solitons for time fractional coupled Zakharov equations","volume":"8","author":"Inc","year":"2022","journal-title":"Int. J. Appl. Comput. Math."},{"key":"ref_24","first-page":"3","article-title":"The Riccati-Bernoulli sub-ODE technique for solving the deterministic (stochastic) generalized-Zakharov system","volume":"1","author":"Abdelrahman","year":"2018","journal-title":"Int. J. Math. Syst. Sci."},{"key":"ref_25","first-page":"101231","article-title":"Computational Analysis and Wave Propagation Behavior of Hyper-Geometric Soliton Waves in Plasma Physics via the Auxiliary Equation Method","volume":"10","author":"Islam","year":"2025","journal-title":"Partial Differ. Equ. Appl. Math."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"537","DOI":"10.1007\/s12648-018-1342-x","article-title":"On the fractional order space-time nonlinear equations arising in plasma physics","volume":"93","author":"Abdou","year":"2019","journal-title":"Indian J. Phys."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"513","DOI":"10.2478\/AMNS.2019.2.00048","article-title":"The new extended rational SGEEM for construction of optical solitons to the (2+1)\u2013dimensional Kundu\u2013Mukherjee\u2013Naskar model","volume":"4","author":"Sulaiman","year":"2019","journal-title":"Appl. Math. Nonlinear Sci."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Kara, S., and Unsal, O. (2022). Implementation of two variable expansion method for extended Jimbo\u2013Miwa equations. J. Ocean Eng. Sci., in Press.","DOI":"10.1016\/j.joes.2022.06.008"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1016\/S0960-0779(02)00321-1","article-title":"A sinh-Gordon equation expansion method to construct doubly periodic solutions for nonlinear differential equations","volume":"16","author":"Yan","year":"2003","journal-title":"Chaos Solitons Fractals"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"106620","DOI":"10.1016\/j.rinp.2023.106620","article-title":"Optical soliton solutions, bifurcation, and stability analysis of the Chen-Lee-Liu model","volume":"51","author":"Islam","year":"2023","journal-title":"Results Phys."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"902","DOI":"10.1016\/j.jmaa.2007.05.066","article-title":"Exclusive Traveling Waves for Competitive Reaction\u2013Diffusion Systems and Their Stabilities","volume":"338","author":"Leung","year":"2008","journal-title":"J. Math. Anal. Appl."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1186\/s13661-024-01825-7","article-title":"Bifurcations, chaotic behavior, sensitivity analysis, and various soliton solutions for the extended nonlinear Schr\u00f6dinger equation","volume":"2024","author":"Sun","year":"2024","journal-title":"Bound. Value Probl."},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Alazman, I., Alkahtani, B.S.T., and Mishra, M.N. (2024). Dynamic of bifurcation, chaotic structure and multi soliton of fractional nonlinear Schr\u00f6dinger equation arise in plasma physics. Sci. Rep., 14.","DOI":"10.1038\/s41598-024-72744-x"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"105526","DOI":"10.1016\/j.cnsns.2020.105526","article-title":"The generalized Duffing oscillator","volume":"93","author":"Kudryashov","year":"2021","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"160","DOI":"10.1016\/0022-1236(87)90044-9","article-title":"Stability Theory of Solitary Waves in the Presence of Symmetry, I","volume":"74","author":"Grillakis","year":"1987","journal-title":"J. Funct. Anal."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1016\/0022-1236(90)90016-E","article-title":"Stability Theory of Solitary Waves in the Presence of Symmetry, II","volume":"94","author":"Grillakis","year":"1990","journal-title":"J. Funct. Anal."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/10\/763\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,17]],"date-time":"2025-10-17T04:15:28Z","timestamp":1760674528000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/10\/763"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,14]]},"references-count":36,"journal-issue":{"issue":"10","published-online":{"date-parts":[[2025,10]]}},"alternative-id":["axioms14100763"],"URL":"https:\/\/doi.org\/10.3390\/axioms14100763","relation":{},"ISSN":["2075-1680"],"issn-type":[{"value":"2075-1680","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,14]]}}}