Further characteristics for certain newly formed solutions for two significant mathematical models by utilization of an efficient semi-analytic method
References
- Hirota R., Exact envelope-soliton solutions of a nonlinear wave equation, Journal of Mathematical Physics, 14(7), 805–809, 1973.
- Maccari A., A generalized Hirota equation in (2+1)-dimensions, Journal of Mathematical Physics, 39(12), 6547–6551, 1998.
- Wazwaz A.M., Abundant soliton and periodic wave solutions for the coupled Higgs field equation, the Maccari system and the Hirota-Maccari system, Physica Scripta, 85(6), 065011, 2012.
- El-Borai M., El-Owaidy H., Ahmed H.M., Arnous A., Soliton solutions of Hirota equation and Hirota-Maccari system, New Trends in Mathematical Sciences, 4(3), 231–238, 2016.
- Wang R., Zhang Y., Chen X.T., Ye R.S., The rational and semi-rational solutions to the Hirota-Maccari system, Nonlinear Dynamics, 100(3), 2767–2778, 2020.
- Mohammed W.W., et al., Exact solutions of Hirota-Maccari system forced by multiplicative noise in the Ito sense, Journal of Low Frequency Noise, Vibration and Active Control, 41(1), 74–84, 2022.
- Han T., Zhao L., Bifurcation, sensitivity analysis and exact traveling wave solutions for the stochastic fractional Hirota-Maccari system, Results in Physics, 47, 106349, 2023.
- Islam M.T., Sarkar T.R., Abdullah F.A., Gomez-Aguilar J., Distinct optical soliton solutions to the fractional Hirota-Maccari system through two separate strategies, Optik, 300, 171656, 2024.
- Tarla S., Ali K.K., Yilmazer R., Yusuf A., Investigation of the dynamical behavior of the Hirota-Maccari system in single-mode fibers, Optical and Quantum Electronics, 54(10), 613, 2022.
- Al-Askar F., Mohammed W.W., Cesarano C., El-Morshedy M., The influence of multiplicative noise and fractional derivative on the solutions of the stochastic fractional Hirota-Maccari system, Axioms, 11(8), 357, 2022.
- Zafar A., et al., Exploring the fractional Hirota-Maccari system for its soliton solutions via impressive analytical strategies, Results in Physics, 43, 106049, 2022.
- Nuruddeen R.I, Multiple soliton solutions for the (3+1) conformable space-time fractional modified Korteweg-de-Vries equations, Journal of Ocean Engineering and Science, 3(1), 11–18, 2018.
- Hashemi M.S., Mirzazadeh M., Ahmad H., A reduction technique to solve the (2+1)-dimensional KdV equations with time local fractional derivatives, Optical and Quantum Electronics, 55, 721, 2023.
- Cheng C.D., Tian B., Zhang C.R., Zhao X., Bilinear form, soliton, breather, hybrid and periodic-wave solutions for a (3+1)-dimensional Korteweg-de Vries equation in a fluid, Nonlinear Dynamics, 105(3), 2525–2538, 2021.
- Akar M., Özkan E.M., On exact solutions of the (2+1)-dimensional time conformable Maccari system, International Journal of Modern Physics B, 37(22), 2350219, 2023.
- Ma W.X., et al., Practical analytical approaches for finding novel optical solitons in the single-mode fibers, Chinese Journal of Physics, 72, 475–486, 2021.
- Usman T., Ullah M.S., Analytical solutions and chaotic insights into the Hirota-Maccari system, Scientific Reports, 15(1), 43540, 2025.
- Baskonus H.M., Mahmud A.A., Muhamad K.A., Tanriverdi T., A study on Caudrey-Dodd-Gibbon-Sawada-Kotera partial differential equation, Mathematical Methods in the Applied Sciences, 45(14), 8737–8753, 2022.
- Akter M., Ullah M.S., Wazwaz A.M., Seadawy A.R., Unveiling Hirota-Maccari model dynamics via diverse elegant methods, Optical and Quantum Electronics, 56(7), 1127, 2024.
- Alotaibi H., Traveling wave solutions to the nonlinear evolution equation using expansion method and addendum to Kudryashov's method, Symmetry, 13(11), 2126, 2021.
- Muhamad K.A., Tanriverdi T., Mahmud A.A., Baskonus H.M., Interaction characteristics of the Riemann wave propagation in the (2+1)-dimensional generalized breaking soliton system, International Journal of Computer Mathematics, 100(6), 1340–1355, 2023.
- Wang H., Analytic solutions to the (3+1)-dimensional modified Korteweg-de Vries-Zakharov-Kuznetsov equation in a plasma by means of Homotopy analysis method, Computational Mathematics and Mathematical Physics, 65(7), 1659–1670, 2025.
- Mahmud A.A., Muhamad K.A., Tanriverdi T., Baskonus H.M., Analyzing soliton dynamics of the solutions of (3+1)-dimensional Gardner-Kadomtsev-Petviashvili model for pulse propagation in single-mode optical fibers, Zeitschrift für angewandte Mathematik und Physik, 77(5), 141, 2026.
- Maccari A., A parametric resonance for the nonlocal Hirota-Maccari equation, Symmetry, 14(7), 1444, 2022.
- Baskonus H.M., Mahmud A.A., Muhamad K.A., Tanriverdi T., Gao W., Studying on Kudryashov-Sinelshchikov dynamical equation arising in mixtures liquid and gas bubbles, Thermal Science, 26(2B), 1229–1244, 2022.
- Ganie A.H., Mofarreh F., Alharthi N.S., Khan A., Novel computations of the time-fractional chemical Schnakenberg mathematical model via non-singular kernel operators, Boundary Value Problems, 2025(2), 1–19, 2025.
- Zhang F., Li P.W., Gu Y., Fan C.M., A space-time generalized finite difference scheme for long wave propagation based on high-order Korteweg-de Vries type equations, Mathematics and Computers in Simulation, 228, 298–312, 2025.
- Abdullah, Rahman G.U., Gómez-Aguilar J.F., Energy balance approach to an optical solitons of (2+1)-dimensional fourth-order Korteweg-de Vries equation with two contemporary integration norms using a new mapping method, Nonlinear Dynamics, 113(10), 11921–11936, 2025.
- Beenish, Samreen M., Bifurcation, multistability, and soliton dynamics in the stochastic potential Korteweg-de Vries equation, International Journal of Theoretical Physics, 64(131), 1–22, 2025.
- Asiedu H.K., Barnes B., Dontwi I.K., Darkwah K.F., Modified semiseparation of variables methods for solving the system of nonlinear fractional partial differential equations, International Journal of Differential Equations, 2025(3634269), 1–15, 2025.
- Meena R.K., Kumar S., Semi-analytical solutions of the multi-dimensional time-fractional solitary water wave equations using RPS method, Mathematical Methods in the Applied Sciences, 48(5), 6208–6221, 2025.
- Mahmud A.A., Tanriverdi T., Muhamad K.A., Baskonus H.M., Characteristic of ion-acoustic waves described in the solutions of the (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation, Journal of Applied Mathematics and Computational Mechanics, 22(2), 36–48, 2023.
- Khalique C.M., Adeyemo O.D., A study of (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation via lie symmetry approach, Results in Physics, 18, 103197, 2020.
- Hamza A.E., et al., Soliton solutions and chaotic dynamics of the ion-acoustic plasma governed by a (3+1)-dimensional generalized Korteweg-de Vries-Zakharov-Kuznetsov equation, Fractal and Fractional, 8(11), 673, 2024.
- Feng C.H., Tian B., Gao X.T., Bilinear form, N solitons, breathers and periodic waves for a (3+1)-dimensional Korteweg-de Vries equation with the time-dependent coefficients in a fluid, Qualitative Theory of Dynamical Systems, 23(Suppl 1), 291, 2024.
- Özdemir N., Agrawal O.P., Karadeniz D., İskender B.B., Fractional optimal control problem of an axis-symmetric diffusion-wave propagation, Physica Scripta, 2009(T136), 014024, 2009.
- Avcı D., İskender Eroğlu B.B., Özdemir N., A heat transfer problem with exponential memory and the associated thermal stresses, Numerical Methods for Partial Differential Equations, 39(1), 231–241, 2023.
- Özdemir N., M-truncated soliton solutions of the fractional(4+1)-dimensional Fokas equation, An International Journal of Optimization and Control: Theories and Applications, 13(1), 123–129, 2023.
- Povstenko Y., Kyrylych T., Axisymmetric fractional diffusion with mass absorption in a circle under time-harmonic impact, Entropy, 24(7), 1002, 2022.
- Wang J., et al., Fractional sub-equation neural networks (fSENNs) method for exact solutions of space-time fractional partial differential equations, Chaos: An Interdisciplinary Journal of Nonlinear Science, 35(4), 043110, 2025.
- Zhang R.F., Bilige S., Bilinear neural network method to obtain the exact analytical solutions of nonlinear partial differential equations and its application to p-gBKP equation, Nonlinear Dynamics, 95, 3041–3048, 2019.
- Mahmud A.A., Muhamad K.A., Tanriverdi T., Dynamical behavior and soliton solutions of the (2+1)-dimensional Novikov-Veselov system of equations, Nonlinear Analysis and Computer Simulations, 1(1), 1, 2026.
- Ahmad M., Naik P.A., Yavuz M., Zada A., Analyzing the soliton waves' behavior in the (3+1)-dimensional time-fractional Jimbo-Miwa equation, Modern Physics Letters B, 40(11), 2650070, 2026.
- Zhang H., Zhang R., Liu Q., A novel multi-modal neurosymbolic reasoning intelligent algorithm for BLMP equation, Chinese Physics Letters, 42(10), 100002, 2025.
- Qawaqneh H., Alsharidi A.K., Exploring the truncated M-fractional exact soliton solutions and modulation instability of the Heimburg model, AIMS Mathematics, 11(3), 8104–8133, 2026.
DOI: https://doi.org/10.2478/ijmce-2026-0022 | Journal eISSN: 2956-7068
Language: English
Submitted on: Nov 21, 2025
Accepted on: May 10, 2026
Published on: Jun 2, 2026
Published by: Harran University
In partnership with: Paradigm Publishing Services
Publication frequency: 2 issues per year
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© 2026 Adnan Ahmad Mahmud, Kalsum Abdulrahman Muhamad, Tanfer Tanriverdi, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.