Exact solutions of the nonlinear heat conduction equation using an analytical approach

Hassan, Inaam Rikan

doi:10.22034/cmde.2025.64393.2920

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	Exact solutions of the nonlinear heat conduction equation using an analytical approach
Computational Methods for Differential Equations
مقاله 24، دوره 14، شماره 1، فروردین 2026، صفحه 348-360 اصل مقاله (855.01 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.64393.2920
نویسنده
Inaam Rikan Hassan^*
University of Information Technology and Communications, (UoITC), Baghdad, Iraq.
چکیده
This paper presents new solutions to the nonlinear heat equation using the Exp-function method. The method employs an exponential form to construct diverse solution models, including one-soliton, two-soliton, hyperbolic, and trigonometric soliton solutions. These solutions are crucial for modeling wave phenomena in studying the stress of water surfaces. By utilizing exponential structures, the complexity of the equation is reduced, and computational efficiency is enhanced. This approach offers a robust framework for solving higher-order nonlinear partial differential equations and explains the behavior of solitons in complex systems.
کلیدواژه‌ها
The Exp-function approach؛ The nonlinear heat equation؛ Solitary and soliton solutions

مراجع
[1] S. Abbasbandy, Approximate solution for the nonlinear model of diffusion and reaction in porous catalysts by means of the homotopy analysis method, Chem. Eng. J., 136 (2008), 144-150. [2] M. A. Abdou, The extended F-expansion method and its application for a class of nonlinear evolution equations, Chaos Solitons Fract., 31 (2007), 95-104. [3] A. Q. Al-Shetwi and M. Z. Sujod, Modeling and simulation of photovoltaic module with enhanced perturb and observe mppt algorithm using matlab/simulink, ARPN J. Eng. Appl. Sci., 11(20) (2016). [4] J. Bona, On solitary waves and their role in the evolution of long waves, Appl. Nonlinear Anal. Boston, MA: Pitman, (1981). [5] F. Bouchaala, M. Y. Ali, and A. Farid, Estimation of compressional seismic wave attenuation of carbonate rocks in Abu Dhabi, United Arab Emirates Comptes Rendus, Geosci., 346(7-8) (2014), 169-178. [6] F. Bouchaala, M. Y. Ali, and J. Matsushima, Attenuation modes from vertical seismic profiling and sonic waveform in a carbonate reservoir, Abu Dhabi, United Arab Emirates, Geophys. Prospecting., 28 (2016), 1030-1047. [7] C. Chun, Solitons and periodic solutions for the fifth-order KdV equation with the Exp-function method, Phys. Let., 372 (2008), 2760-2766. [8] C. Q. Dai and J. F. Zhang, Jacobian elliptic function method for nonlinear differential-difference equations, Chaos Solitons Fract., 27 (2006), 1042-1049. [9] M. Dehghan and J. Manafian, The solution of the variable coefficients fourth–order parabolic partial differential equations by homotopy perturbation method, Z. Naturforschung A, 64(a) (2009), 420-430. [10] M. Dehghan, J. Manafian, and A. Saadatmandi, Solving nonlinear fractional partial differential equations using the homotopy analysis method, Num. Meth. Partial Diff. Eq., 26 (2010), 448-479. [11] M. Dehghan, J. M. Heris, and A. Saadatmandi, Application of the Exp-function method for solving a partial differential equation arising in biology and population genetics, Int. J. Num. Meth. Heat Fluid Flow, 21(6) (2011), 736-753. [12] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Let. A, 277 (2000), 212-218. [13] Y. S. Gasimov, A. Nachaoui, and A. A. Niftiyev, Non-linear eigenvalue problems for p-Laplacian with variable domain, Optimiz. Let., 4 (2010), 67-84. [14] Y. Gu, S. Malmir, J. Manafian, O. A. Ilhan, A. A. Alizadeh, and A. J. Othman, Variety interaction between k-lump and k-kink solutions for the (3+1)-D Burger system by bilinear analysis, Results Phys., 43 (2022), 106032. [15] M. A. Haowei, U. A. R. Hussein, Z. H. Al-Qaim, F. M. Altalbawy, A. A. Fadhil, M. M. Al-Taee, and M. Hekmatifar, Employing Sisko non-Newtonian model to investigate the thermal behavior of blood flow in a stenosis artery: Effects of heat flux, different severities of stenosis, and different radii of the artery, Alexandria Eng. J., 68 (2023), 291-300. [16] J. H. He, Non-perturbative method for strongly nonlinear problems. Dissertation, De-Verlag im Internet GmbH, Berlin, (2006).a [17] J. H. He, Variational iteration method a kind of non-linear analytical technique: some examples, International J. Non-Linear Mech., 34 (1999), 699-708. [18] J. H. He and X.H. Wu, Exp–function method for nonlinear wave equations, Chaos Solitons Fract., 30 (2006), 700-708. [19] D. A. Juraev and Y. S. Gasimov, On the regularization Cauchy problem for matrix factorizations of the Helmholtz equation in a multidimensional bounded domain, Azerbaijan J. Math., 12(1) (2022), 142-161. [20] N. A. Kudryashov and N. B. Loguinova, Be careful with the Exp-function method, Communic. Nonlinear Sci. Num. Simul., 14 (2009), 1881-1890. [21] M. Lakestani, J. Manafian, A. R. Najafizadeh, and M. Partohaghighi, Some new soliton solutions for the nonlinear the fifth-order integrable equations, Comput. Meth. Diff. Eq., 10(2) (2022), 445-460. [22] H. Ma, Research on promotion of lower limb movement function recovery after stroke by using lower limb rehabilitation robot in combination with constant velocity muscle strength training, In 2021 7th Int. Symp. Mechat. Indust. Inform., (2021), 70-73. [23] J. Manafian, L. A. Dawood, and M. Lakestani, New solutions to a generalized fifth-order KdV like equation with prime number p = 3 via a generalized bilinear differential operator, Partial Diff. Eq. Appl. Math., 9 (2024), 100600. [24] J. Manafian, O. A. Ilhan, A. Alizadeh, and S. A. Mohammed, Multiple rogue wave and solitary solutions for the generalized BK equation via Hirota bilinear and SIVP schemes arising in fluid mechanics, Commun. Theo. Phys., 72 (2020), 075002. [25] J. Manafian and M. Lakestani, N-lump and interaction solutions of localized waves to the (2+1)-dimensional variable-coefficient Caudrey-Dodd-Gibbon-Kotera-Sawada equation, J. Geom. Phys., 150 (2020), 103598. [26] J. Manafian and M. Lakestani, Application of tan(ϕ/2)-expansion method for solving the Biswas-Milovic equation for Kerr law nonlinearity, Optik, 127(4) (2016), 2040-2054. [27] J. Manafian and M. Lakestani, Optical soliton solutions for the Gerdjikov-Ivanov model via tan(ϕ/2)-expansion method, Optik, 127(20) (2016), 9603-9620. [28] J. Manafian and M. Lakestani, Abundant soliton solutions for the Kundu-Eckhaus equation via tan(ϕ(ξ))expansion method, Optik, 127(14) (2016), 5543-5551. [29] M. J. Mardanov, Y. A. Sharifov, Y. S. Gasimov, and C. Cattani, Non-linear first-order differential boundary problems with multipoint and integral conditions, Frac. Fract., 5(1) (2021), 15. [30] S. Micu, On the controllability of the linearized Benjamin-Bona-Mahony equation, SIAM J. Control Optimiz., 29 (2005), 1677-1696. [31] S. R. Moosavi, N. Taghizadeh, and J. Manafian, Analytical approximations of one-dimensional hyperbolic equation with non-local integral conditions by reduced differential transform method, Comput. Meth. Diff. Eq., 8(3) (2020), 537-552. [32] X. Shen, J. Manafian, M. Jiang, O. A. Ilhan, S. S. Shafik, and M. Zaidi, Abundant wave solutions for generalized Hietarinta equation with Hirota’s bilinear operator, Modern Phys. Let. B, 36(10) (2022), 2250032. [33] A. M. Wazwaz, Solitary wave solutions of the generalized shallow water wave (GSWW) equation by Hirota’s method, tanh-coth method and Exp-function method, Appl. Math. Comput., 202 (2008), 275-286. [34] A. M. Wazwaz, The tanh method for generalized forms of nonlinear heat conduction and Burgers-Fisher equations, Appl. Math. Computat., 169 (2005), 321-338. [35] X. H. Wu and J. H. He, Exp-function method and its application to nonlinear equations, Chaos Solitons Fract., 38 (2008), 903-910.
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Exact solutions of the nonlinear heat conduction equation using an analytical approach