Application of homotopy perturbation method to nonlinear wave equations
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Cited by:
- Biazar, J. & Ghazvini, H., 2009. "He’s homotopy perturbation method for solving systems of Volterra integral equations of the second kind," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 770-777.
- Alipanah, Amjad & Zafari, Mahnaz, 2023. "Collocation method using auto-correlation functions of compact supported wavelets for solving Volterra’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
- Tang, Yaning & Xu, Wei & Shen, Jianwei & Gao, Liang, 2008. "Persistence of solitary wave solutions of singularly perturbed Gardner equation," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 532-538.
- Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
- Siddiqui, A.M. & Ahmed, M. & Ghori, Q.K., 2007. "Thin film flow of non-Newtonian fluids on a moving belt," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1006-1016.
- Javidi, M. & Golbabai, A., 2009. "A new domain decomposition algorithm for generalized Burger’s–Huxley equation based on Chebyshev polynomials and preconditioning," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 849-857.
- Shidfar, A. & Molabahrami, A. & Babaei, A. & Yazdanian, A., 2009. "A study on the d-dimensional Schrödinger equation with a power-law nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2154-2158.
- Ramos, J.I., 2009. "Piecewise-adaptive decomposition methods," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1623-1636.
- Seadawy, Aly R., 2015. "Nonlinear wave solutions of the three-dimensional Zakharov–Kuznetsov–Burgers equation in dusty plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 439(C), pages 124-131.
- Alomari, A.K. & Noorani, M.S.M. & Nazar, R., 2009. "On the homotopy analysis method for the exact solutions of Helmholtz equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1873-1879.
- Hassan A. Zedan & Eman El Adrous, 2012. "The Application of the Homotopy Perturbation Method and the Homotopy Analysis Method to the Generalized Zakharov Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
- Javidi, M. & Golbabai, A., 2009. "Modified homotopy perturbation method for solving non-linear Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1408-1412.
- Meshari Alesemi & Naveed Iqbal & Thongchai Botmart, 2022. "Novel Analysis of the Fractional-Order System of Non-Linear Partial Differential Equations with the Exponential-Decay Kernel," Mathematics, MDPI, vol. 10(4), pages 1-17, February.
- Batiha, B. & Noorani, M.S.M. & Hashim, I., 2008. "Application of variational iteration method to the generalized Burgers–Huxley equation," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 660-663.
- Yusufoğlu (Agadjanov), Elcin, 2009. "Improved homotopy perturbation method for solving Fredholm type integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 28-37.
- A. A. Hemeda, 2014. "Modified Homotopy Perturbation Method for Solving Fractional Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
- Yanqin Liu, 2012. "Approximate Solutions of Fractional Nonlinear Equations Using Homotopy Perturbation Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
- Mohamed. Z. Mohamed & Mohammed Yousif & Amjad E. Hamza, 2022. "Solving Nonlinear Fractional Partial Differential Equations Using the Elzaki Transform Method and the Homotopy Perturbation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2022(1).
- Ucar, Y. & Karaagac, B. & Esen, A., 2015. "A new approach on numerical solutions of the Improved Boussinesq type equation using quadratic B-spline Galerkin finite element method," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 148-155.
- Mehmet Merdan & Ahmet Gökdoğan & Ahmet Yıldırım & Syed Tauseef Mohyud-Din, 2012. "Numerical Simulation of Fractional Fornberg‐Whitham Equation by Differential Transformation Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
- Jiong Weng & Xiaojing Liu & Youhe Zhou & Jizeng Wang, 2021. "A Space-Time Fully Decoupled Wavelet Integral Collocation Method with High-Order Accuracy for a Class of Nonlinear Wave Equations," Mathematics, MDPI, vol. 9(22), pages 1-17, November.
- Shumaila Javeed & Dumitru Baleanu & Asif Waheed & Mansoor Shaukat Khan & Hira Affan, 2019. "Analysis of Homotopy Perturbation Method for Solving Fractional Order Differential Equations," Mathematics, MDPI, vol. 7(1), pages 1-14, January.
- Ravi Kanth, A.S.V. & Aruna, K., 2009. "He’s homotopy-perturbation method for solving higher-order boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1905-1909.
- Abdolamir Karbalaie & Hamed Hamid Muhammed & Bjorn-Erik Erlandsson, 2013. "Using Homo-Separation of Variables for Solving Systems of Nonlinear Fractional Partial Differential Equations," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2013, pages 1-8, June.
- Yildirim, Ahmet, 2009. "Homotopy perturbation method for the mixed Volterra–Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2760-2764.
- Abbasbandy, S., 2006. "Application of He’s homotopy perturbation method for Laplace transform," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1206-1212.
- Ji-Huan He, 2012. "Asymptotic Methods for Solitary Solutions and Compactons," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
- Hossein Aminikhah & Farshid Mehrdoust & Ali Jamalian, 2012. "A New Efficient Method for Nonlinear Fisher‐Type Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
- Cveticanin, L., 2009. "Application of homotopy-perturbation to non-linear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 221-228.
- S. S. Nourazar & M. Habibi Matin & M. Simiari, 2011. "The HPM Applied to MHD Nanofluid Flow over a Horizontal Stretching Plate," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
- Chowdhury, M.S.H. & Hashim, I. & Momani, S., 2009. "The multistage homotopy-perturbation method: A powerful scheme for handling the Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1929-1937.
- Shweta, & Arora, Gourav & Kumar, Rajesh, 2025. "Large time solution for collisional breakage model: Laplace transformation based accelerated homotopy perturbation method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 230(C), pages 39-52.
- Gordoa, P.R., 2007. "A note on solutions of an equation modelling arterial deformation," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1505-1511.
- Mohamed S. Mohamed & Khaled A. Gepreel & Faisal A. Al-Malki & Nouf Altalhi, 2014. "Extension of Khan’s Homotopy Transformation Method via Optimal Parameter for Differential Difference Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
- Hector Vazquez-Leal & Arturo Sarmiento-Reyes & Yasir Khan & Uriel Filobello-Nino & Alejandro Diaz-Sanchez, 2012. "Rational Biparameter Homotopy Perturbation Method and Laplace‐Padé Coupled Version," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
- He, Ji-Huan & Wu, Xu-Hong, 2006. "Construction of solitary solution and compacton-like solution by variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 29(1), pages 108-113.
- Sadaf, Hina & Akbar, Muhammad Usman & Nadeem, S., 2018. "Induced magnetic field analysis for the peristaltic transport of non-Newtonian nanofluid in an annulus," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 16-36.
- Tariq, Kalim U. & Bekir, Ahmet & Nisar, Sana, 2023. "The dynamical structures of the Sharma–Tasso–Olver model in doubly dispersive medium," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
- Ahmad Sami Bataineh & Osman Rasit Isik & Abedel-Karrem Alomari & Mohammad Shatnawi & Ishak Hashim, 2020. "An Efficient Scheme for Time-Dependent Emden-Fowler Type Equations Based on Two-Dimensional Bernstein Polynomials," Mathematics, MDPI, vol. 8(9), pages 1-17, September.
- Duan, Zhisheng & Wang, Jinzhi & Yang, Ying & Huang, Lin, 2009. "Frequency-domain and time-domain methods for feedback nonlinear systems and applications to chaos control," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 848-861.
- Younghae Do & Bongsoo Jang, 2012. "Nonlinear Klein‐Gordon and Schrödinger Equations by the Projected Differential Transform Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
- Hassan A. Zedan & W. Barakati & Nada Hamad, 2013. "The Application of the Homotopy Analysis Method and the Homotopy Perturbation Method to the Davey‐Stewartson Equations and Comparison between Them and Exact Solutions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
- Hradyesh Kumar Mishra & Atulya K. Nagar, 2012. "He‐Laplace Method for Linear and Nonlinear Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
- Mei, Shu-Li & Du, Cheng-Jin & Zhang, Sen-Wen, 2008. "Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 536-542.
- Mossa Al-sawalha, M. & Noorani, M.S.M., 2009. "A numeric–analytic method for approximating the chaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1784-1791.
- Shu-Li Mei, 2013. "Construction of Target Controllable Image Segmentation Model Based on Homotopy Perturbation Technology," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
- Héctor Vázquez-Leal, 2012. "Rational Homotopy Perturbation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
- Lv, Jian Cheng & Yi, Zhang, 2007. "Some chaotic behaviors in a MCA learning algorithm with a constant learning rate," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1040-1047.
- Biazar, J. & Eslami, M. & Aminikhah, H., 2009. "Application of homotopy perturbation method for systems of Volterra integral equations of the first kind," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3020-3026.
- Öziş, Turgut & Yıldırım, Ahmet, 2007. "Determination of limit cycles by a modified straightforward expansion for nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 445-448.
- Cai, Xu-Chu & Wu, Wen-Ying, 2009. "Homotopy perturbation method for nonlinear oscillator equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2581-2583.
- Masoud Mosaddeghi, 2014. "[Retracted] Bifurcation of Travelling Wave Solutions of the Generalized Zakharov Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
- Xu, Lan, 2008. "Variational approach to solitons of nonlinear dispersive K(m,n) equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 137-143.
- Mădălina Sofia Paşca & Olivia Bundău & Adina Juratoni & Bogdan Căruntu, 2022. "The Least Squares Homotopy Perturbation Method for Systems of Differential Equations with Application to a Blood Flow Model," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
- Beléndez, A. & Beléndez, T. & Márquez, A. & Neipp, C., 2008. "Application of He’s homotopy perturbation method to conservative truly nonlinear oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 770-780.
- Taher A. Nofal, 2012. "Approximate Solutions for Nonlinear Initial Value Problems Using the Modified Variational Iteration Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
- Keramati, B., 2009. "An approach to the solution of linear system of equations by He’s homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 152-156.
- Al-Khaled, Kamel, 2007. "Theory and computation in singular boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 678-684.
- He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
- Emad H. Aly & Abdelhalim Ebaid, 2013. "New Analytical and Numerical Solutions for Mixed Convection Boundary‐Layer Nanofluid Flow along an Inclined Plate Embedded in a Porous Medium," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
- Wu, Tzong-Mou, 2007. "The secant–homotopy continuation method," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 888-892.
- Duan, Yali & Kong, Linghua & Zhang, Rui, 2012. "A lattice Boltzmann model for the generalized Burgers–Huxley equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 625-632.
- Allan, Fathi M., 2009. "Construction of analytic solution to chaotic dynamical systems using the Homotopy analysis method," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1744-1752.
- Abbasbandy, S., 2007. "A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 257-260.
- Çelik, Nisa & Seadawy, Aly R. & Sağlam Özkan, Yeşim & Yaşar, Emrullah, 2021. "A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
- Mingsheng Hu & Zhijuan Jia & Qiaoling Chen & Suiming Jia, 2014. "Exact Solutions for Nonlinear Wave Equations by the Exp‐Function Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
- Xu, Wei & Shen, Jianwei, 2008. "Solitary and periodic traveling wave solutions for a class of coupled nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 912-917.
- Dianchen Lu & Jie Liu, 2014. "Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV‐Burgers Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
- Ghorbani, Asghar, 2009. "Beyond Adomian polynomials: He polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1486-1492.
- Odibat, Zaid M., 2009. "Exact solitary solutions for variants of the KdV equations with fractional time derivatives," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1264-1270.
- Hashim, I. & Chowdhury, M.S.H. & Mawa, S., 2008. "On multistage homotopy-perturbation method applied to nonlinear biochemical reaction model," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 823-827.
- Abdelfattah El Achab, 2014. "Elliptic Travelling Wave Solutions to a Generalized Boussinesq Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
- Mubashir Qayyum & Farnaz Ismail & Syed Inayat Ali Shah & Muhammad Sohail & Kanayo Kenneth Asogwa & Fatema Tuz Zohra, 2022. "Analysis of Fractional Thin Film Flow of Third Grade Fluid in Lifting and Drainage via Homotopy Perturbation Procedure," Advances in Mathematical Physics, John Wiley & Sons, vol. 2022(1).
- Borhanifar, A. & Kabir, M.M. & Maryam Vahdat, L., 2009. "New periodic and soliton wave solutions for the generalized Zakharov system and (2+1)-dimensional Nizhnik–Novikov–Veselov system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1646-1654.
- Siddiqui, A.M. & Mahmood, R. & Ghori, Q.K., 2008. "Homotopy perturbation method for thin film flow of a third grade fluid down an inclined plane," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 140-147.
- Demiray, Hilmi, 2006. "Interaction of nonlinear waves governed by Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1185-1189.
- M. S. H. Chowdhury & I. Hashim & S. Momani & M. M. Rahman, 2012. "Application of Multistage Homotopy Perturbation Method to the Chaotic Genesio System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
- E. E. Eladdad & E. A. Tarif, 2019. "On the Coupling of the Homotopy Perturbation Method and New Integral Transform for Solving Systems of Partial Differential Equations," Advances in Mathematical Physics, John Wiley & Sons, vol. 2019(1).
- Javidi, M. & Golbabai, A., 2008. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the variational iteration method," Chaos, Solitons & Fractals, Elsevier, vol. 36(2), pages 309-313.
- Mahmoud, Abeer A. & Tolba, R.E., 2019. "Nonlinear dust-acoustic waves due to the interaction of streaming protons and electrons with dusty plasma," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 320-327.
- Alim, Md. Abdul & Kawser, M. Abul, 2023. "Illustration of the homotopy perturbation method to the modified nonlinear single degree of freedom system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
- Alessandra Jannelli, 2020. "Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
- He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
- Wenbin Zhang & Jiangbo Zhou & Lixin Tian & Sunil Kumar, 2013. "On the Support of Solutions to a Two-Dimensional Nonlinear Wave Equation," Journal of Mathematics, Hindawi, vol. 2013, pages 1-4, March.
- Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
- Yu, Jun & Zhang, Weijun & Gao, Xiaoming, 2007. "Dynamical behavior in the perturbed compound KdV–Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1307-1313.
- Odibat, Zaid & Momani, Shaher, 2008. "Modified homotopy perturbation method: Application to quadratic Riccati differential equation of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 167-174.
- Yu, Guo-Fu & Tam, Hon-Wah, 2006. "Conservation laws for two (2+1)-dimensional differential–difference systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 189-196.
- Sheng, Zhang, 2007. "The periodic wave solutions for the (2+1)-dimensional dispersive long water equations," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 847-854.
- Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.
- Gui-qiong Xu, 2014. "Extended Auxiliary Equation Method and Its Applications to Three Generalized NLS Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
- Shuang-Shuang Zhou & Nehad Ali Shah & Ioannis Dassios & S. Saleem & Kamsing Nonlaopon, 2021. "A Comparative Analysis of Fractional-Order Gas Dynamics Equations via Analytical Techniques," Mathematics, MDPI, vol. 9(15), pages 1-15, July.
- Öziş, Turgut & Yıldırım, Ahmet, 2007. "A note on He’s homotopy perturbation method for van der Pol oscillator with very strong nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 989-991.
- Hegagi Mohamed Ali & Ismail Gad Ameen, 2019. "An Efficient Approach for Solving Fractional Dynamics of a Predator-Prey System," Modern Applied Science, Canadian Center of Science and Education, vol. 13(11), pages 116-116, November.
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- Siddiqui, A.M. & Zeb, A. & Ghori, Q.K. & Benharbit, A.M., 2008. "Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 182-192.
- Goh, S.M. & Noorani, M.S.M. & Hashim, I., 2009. "A new application of variational iteration method for the chaotic Rössler system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1604-1610.
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- Mubashir Qayyum & Aneeqa Bilal & Omar Khan & Saraswati Acharya, 2025. "Analysis of Fuzzy‐Fractional Fornberg–Whitham Models Using Extended He‐Laplace Methodology," Journal of Mathematics, John Wiley & Sons, vol. 2025(1).
- Abbasbandy, S., 2007. "Application of He’s homotopy perturbation method to functional integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1243-1247.
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- Nabard Habibi & Zohre Nouri, 2020. "Application of Local Fractional Homotopy Perturbation Method in Physical Problems," Advances in Mathematical Physics, John Wiley & Sons, vol. 2020(1).
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