Triangular Fuzzy Solutions of Coupled Boussinesq-Burgers Equations with Uncertain Parameters

[1] H. Abdel-Gawad, M. Tantawy, On controlled propagation of long waves in nonautonomous boussinesq-burgers equations, Nonlinear Dynamics, 87 (2017), 2511-2518. https://doi.org/10.1007/s11071-016-3207-1

[2] Z. Ayati, J. Biazar, On the convergence of homotopy perturbation method, Journal of the Egyptian Mathematical
Society, 23(2) (2015), 424-428. https://doi.org/10.1016/j.joems.2014.06.015

[3] M. Benosman, J. Borggaard, O. San, B. Kramer, Learning-based robust stabilization for reduced-order models of 2d
and 3d boussinesq equations, Applied Mathematical Modelling, 49 (2017), 162-181. https://doi.org/10.1016/j.
apm.2017.04.032

[4] M. J. Dong, S. F. Tian, X. W. Yan, T. T. Zhang, Nonlocal symmetries, conservation laws and interaction solutions
for the classical boussinesq-burgers equation, Nonlinear Dynamics, 95 (2019), 273-291. https://doi.org/10.1007/
s11071-018-4563-9

[5] Z. Eidinejad, R. Saadati, C. Li, M. Inc, J. Vahidi, The multiple exp-function method to obtain soliton solutions of
the conformable date-jimbo-kashiwara-miwa equations, International Journal of Modern Physics B, 38(03) (2024),
2450043. https://doi.org/10.1142/S0217979224500437

[6] Z. Eidinejad, R. Saadati, J. Vahidi, C. Li, Numerical solutions of 2d stochastic time-fractional sine-gordon equation
in the caputo sense, International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, 36(6)
(2023), e3121. https://doi.org/10.1002/jnm.3121

[7] T. M. Elzaki, The new integral transform Elzaki transform, Global Journal of Pure and Applied Mathematics, 7(1)
(2011), 57-64. https://www.researchgate.net/publication/289123241

[8] T. M. Elzaki, Application of new transform “Elzaki Transform” to partial differential equations, Global Journal of
Pure and Applied Mathematics, 7(1) (2011), 65-70. https://www.researchgate.net/publication/236230758

[9] T. M. Elzaki, S. M. Elzaki, E. A. Elnour, On the new integral transform “Elzaki Transform” fundamental properties
investigations and applications, Global Journal of Mathematical Sciences: Theory and Practical, 4(1) (2012), 1-13.
https://www.researchgate.net/publication/258316406

[10] X. Y. Gao, Y. J. Guo, W. R. Shan, Beholding the shallow water waves near an ocean beach or in a lake via a
boussinesq-burgers system, Chaos, Solitons and Fractals, 147 (2021), 110875. https://doi.org/10.1016/j.chaos.
2021.110875

[11] X. Y. Gao, Y. J. Guo, W. R. Shan, On the oceanic/laky shallow-water dynamics through a boussinesqburgers
system, Qualitative Theory of Dynamical Systems, 23(2) (2024), 57. https://doi.org/10.1007/
s12346-023-00905-w

[12] X. T. Gao, B. Tian, T. Y. Zhou, Y. Shen, C. H. Feng, For the shallow water waves: Bilinear-form and similarityreduction
studies on a boussinesq-burgers system, International Journal of Theoretical Physics, 63(7) (2024), 179.
https://doi.org/10.1007/s10773-024-05715-7

[13] P. Guo, X. Wu, L. Wang, New multiple-soliton (kink) solutions for the high-order boussinesq-burgers equation,
Waves in Random and Complex Media, 26(3) (2016), 383-396. https://doi.org/10.1080/17455030.2016.
1158885

[14] A. Gupta, S. S. Ray, Comparison between homotopy perturbation method and optimal homotopy asymptotic method
for the soliton solutions of boussinesq-burger equations, Computers and Fluids, 103 (2014), 34-41. https://doi.
org/10.1016/j.compfluid.2014.07.008q

[15] O. E. Ige, R. A. Oderinu, T. M. Elzaki, Adomian polynomial and elzaki transform method for solving klein gordon
equations, International Journal of Applied Mathematics, 32(3) (2019), 451. https://www.researchgate.net/
publication/335276371

[16] Y. L. Jiang, C. Chen, Lie group analysis and dynamical behavior for classical boussinesq-burgers system, Nonlinear
Analysis: Real World Applications, 47 (2019), 385-397. https://doi.org/10.1016/j.nonrwa.2018.11.010

[17] P. Karunakar, S. Chakraverty, Effect of coriolis constant on geophysical korteweg-de vries equation, Journal of
Ocean Engineering and Science, 4(2) (2019), 113-121. https://doi.org/10.1016/j.joes.2019.02.002

[18] P. Karunakar, S. Chakraverty, Homotopy perturbation method for predicting tsunami wave propagation with crisp
and uncertain parameters, International Journal of Numerical Methods for Heat and Fluid Flow, 31(1) (2020),
92-105. https://doi.org/10.1108/HFF-11-2019-0861

[19] P. Karunakar, S. Chakraverty, T. Rao, K. Ramesh, A. Hussein, Fuzzy fractional shallow water wave equations:
Analysis, convergence of solutions, and comparative study with depth as triangular fuzzy number, Physica Scripta,
99(12) (2024), 125216. https://doi.org/10.1088/1402-4896/ad8afd

[20] M. Khalfallah, Exact traveling wave solutions of the boussinesq-burgers equation, Mathematical and Computer
Modelling, 49(3-4) (2009), 666-671. https://doi.org/10.1016/j.mcm.2008.08.004

[21] R. Kumar, K. S. Pandey, A. Kumar, Dynamical behavior of the solutions of coupled boussinesq-burgers equations
occurring at the seaside beaches, Brazilian Journal of Physics, 52(6) (2022), 201. https://doi.org/10.1007/
s13538-022-01195-4

[22] S. Kumar, S. Rani, Symmetries of optimal system, various closed-form solutions, and propagation of different wave
profiles for the boussinesq-burgers system in ocean waves, Physics of Fluids, 34(3) (2022). https://doi.org/10.
1063/5.0085927

[23] X. Li, A. Chen, Darboux transformation and multi-soliton solutions of boussinesq-burgers equation, Physics Letters
A, 342(5-6) (2005), 413-420. https://doi.org/10.1016/j.physleta.2005.05.083

[24] M. Li, W. Hu, C.Wu, Rational solutions of the classical boussinesq-burgers system, Nonlinear Dynamics, 94 (2018),
1291-1302. https://doi.org/10.1007/s11071-018-4424-6

[25] Z. Liang, Z. L. Feng, L. C. Yin, Some new exact solutions of Jacobian elliptic function about the generalized
boussinesq equation and boussinesq-burgers equation, Chinese Physics B, 17(2) (2008), 403. https://doi.org/10.
1088/1674-1056/17/2/009

[26] F. Y. Liu, Y. T. Gao, Lie group analysis for a higher-order boussinesq-burgers system, Applied Mathematics Letters,
132 (2022), 108094. https://doi.org/10.1016/j.aml.2022.108094

[27] M. Liu, H. Xu, Z.Wang, Exact solutions and bifurcations of the time-fractional coupled boussinesq-burgers equation,
Physica Scripta, 98(11) (2023), 115040. https://doi.org/10.1088/1402-4896/ad03c4

[28] J. Lu, Y. Sun, Numerical approaches to time fractional boussinesq-burgers equations, Fractals, 29(08) (2021),
2150244. https://doi.org/10.1142/S0218348X21502443

[29] B. A. Mahmood, M. A. Yousif, A residual power series technique for solving boussinesq-burgers equations, Cogent
Mathematics, 4(1) (2017), 1279398. https://doi.org/10.1080/23311835.2017.1279398

[30] A. M. Mubaraki, R. Nuruddeen, K. K. Ali, J. G´omez-Aguilar, Additional solitonic and other analytical solutions
for the higher-order boussinesq-burgers equation, Optical and Quantum Electronics, 56(2) (2024), 165. https:
//doi.org/10.1007/s11082-023-05744-2

[31] Z. M. Odibat, A study on the convergence of homotopy analysis method, Applied Mathematics and Computation,
217(2) (2010), 782-789. https://doi.org/10.1016/j.amc.2010.06.017

[32] A. Podder, M. A. Arefin, K. A. Gepreel, M. H. Uddin, M. A. Akbar, Diverse soliton wave profile assessment to
the fractional order nonlinear landau-ginzburg-higgs and coupled boussinesq-burger equations, Results in Physics, 65
(2024), 107994. https://doi.org/10.1016/j.rinp.2024.107994

[33] A. A. Rady, M. Khalfallah, On soliton solutions for boussinesq-burgers equations, Communications in Nonlinear
Science and Numerical Simulation, 15(4) (2010), 886-894. https://doi.org/10.1016/j.cnsns.2009.05.039

[34] A. A. Rady, E. Osman, M. Khalfallah, Multi-soliton solution, rational solution of the boussinesq-burgers equations,
Communications in Nonlinear Science and Numerical Simulation, 15(5) (2010), 1172-1176. https://doi.org/10.
1016/j.cnsns.2009.05.053

[35] P. Rao, D. Mohapatra, S. Chakraverty, D. Roy, Vibration analysis of non-homogenous single-link flexible manipulator
in uncertain environment, Applied Mathematical Modelling, (2025), 115939. https://doi.org/10.1016/j.
apm.2025.115939

[36] X. Rui, Darboux transformations and soliton solutions for classical boussinesq-burgers equation, Communications
in Theoretical Physics, 50(3) (2008), 579. https://doi.org/10.1088/0253-6102/50/3/08

[37] M. Sahoo, S. Chakraverty, Dynamics of tsunami wave propagation in uncertain environment, Computational and
Applied Mathematics, 43(5) (2024), 266. https://doi.org/10.1007/s40314-024-02776-6

[38] D. Shi, Y. Zhang, W. Liu, J. Liu, Some exact solutions and conservation laws of the coupled time-fractional
boussinesq-burgers system, Symmetry, 11(1) (2019), 77. https://doi.org/10.3390/sym11010077

[39] R. Vana, P. Karunakar, A fuzzy semi-analytical approach for modeling uncertainties in solitary wave solution
of coupled nonlinear boussinesq equations, Physica Scripta, 99(10) (2024), 105218. https://doi.org/10.1088/
1402-4896/ad72aa

[40] R. Vana, P. Karunakar, Computational approach and convergence analysis for intervalbased solution of the
benjamin-bona-mahony equation with imprecise parameters, Engineering Computations: International Journal for
Computer-Aided Engineering, 41(4) (2024), 1067-1085. https://doi.org/10.1108/EC-12-2023-0905

[41] R. Vana, P. Karunakar, Fuzzy uncertainty modeling of generalized hirota-satsuma coupled korteweg-de vries equation,
Physics of Fluids, 36(9) (2024), 096609. https://doi.org/10.1063/5.0226445

[42] R. Vana, P. Karunakar, Uncertainties in regularized long-wave equation and its modified form: A triangular fuzzybased
approach, Physics of Fluids, 36(4) (2024), 046610. https://doi.org/10.1063/5.0206452

[43] R. Vana, K. Perumandla, S. Chakraverty, Semi-analytical and numerical computations for the solution of uncertain
fractional benjamin bona mahony equation with triangular fuzzy number, Journal of Computational Applied
Mechanics, 56(1) (2025), 196-221. https://doi.org/10.22059/jcamech.2024.387317.1318

[44] A. C. Varsoliwala, T. R. Singh, An approximate analytical solution of non linear partial differential equation for
water infiltration in unsaturated soils by combined elzaki transform and adomian decomposition method, in: Journal
of Physics: Conference Series, Vol. 1473, IOP Publishing, (2020), 012009. https://doi.org/10.1088/1742-6596/
1473/1/012009

[45] A. C. Varsoliwala, T. R. Singh, Mathematical modeling of tsunami wave propagation at mid ocean and its
amplification and run-up on shore, Journal of Ocean Engineering and Science, 6(4) (2021), 367-375. https:
//doi.org/10.1016/j.joes.2021.03.003

[46] A. C. Varsoliwala, T. R. Singh, Solution of fingering phenomenon arising in porous media in horizontal direction
by combination of elzaki transform and adomian decomposition method, in: Advances in Mathematical Modelling,
Applied Analysis and Computation: Proceedings of ICMMAAC 2021, Springer, (2022), 495-506. https://doi.
org/10.1007/978-981-19-0179-9_29

[47] A. C. Varsoliwala, T. R. Singh, Mathematical modeling of atmospheric internal waves phenomenon and its solution
by elzaki adomian decomposition method, Journal of Ocean Engineering and Science, 7(3) (2022), 203-212. https:
//doi.org/10.1016/j.joes.2021.07.010

[48] Y. H.Wang, CTE method to the interaction solutions of boussinesq-burgers equations, Applied Mathematics Letters,
38 (2014), 100-105. https://doi.org/10.1016/j.aml.2014.07.014

[49] K. J. Wang, G. D. Wang, H. W. Zhu, A new perspective on the study of the fractal coupled boussinesq-burger
equation in shallow water, Fractals, 29(05) (2021), 2150122. https://doi.org/10.1142/S0218348X2150122X

[50] C. C. Zhang, A. H. Chen, Bilinear form and new multi-soliton solutions of the classical boussinesq-burgers system,
Applied Mathematics Letters, 58 (2016), 133-139. https://doi.org/10.1016/j.aml.2016.02.015

[51] Y. Zhang, L. Wang, Application of laplace adomian decomposition method for fractional fokker-planck equation
and time fractional coupled boussinesq-burger equations, Engineering Computations, 41(4) (2024), 793-818. https:
//doi.org/10.1108/EC-06-2023-0275

[52] P. M. Zu, X. M. Zhang, Study of the generalized hypothetical syllogism for some well known families of fuzzy
implications with respect to strict t-norm, Iranian Journal of Fuzzy Systems, 21(2) (2024), 181-200. https://doi.
org/10.22111/ijfs.2024.46361.8164

[53] J. M. Zuo, Y. M. Zhang, The hirota bilinear method for the coupled burgers equation and the high-order boussinesqburgers equation, Chinese Physics B, 20(1) (2011), 010205. https://doi.org/10.1088/1674-1056/20/1/010205