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Application of homotopy perturbation method to nonlinear wave equations

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  1. 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.
  2. 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).
  3. 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.
  4. 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.
  5. 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.
  6. 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.
  7. 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.
  8. Ramos, J.I., 2009. "Piecewise-adaptive decomposition methods," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1623-1636.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. 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.
  14. 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.
  15. 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.
  16. 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.
  17. 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.
  18. 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.
  19. 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.
  20. Yildirim, Ahmet, 2009. "Homotopy perturbation method for the mixed Volterra–Fredholm integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2760-2764.
  21. Abbasbandy, S., 2006. "Application of He’s homotopy perturbation method for Laplace transform," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1206-1212.
  22. Cveticanin, L., 2009. "Application of homotopy-perturbation to non-linear partial differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 221-228.
  23. 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.
  24. Gordoa, P.R., 2007. "A note on solutions of an equation modelling arterial deformation," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1505-1511.
  25. 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.
  26. 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.
  27. 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).
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. Cai, Xu-Chu & Wu, Wen-Ying, 2009. "Homotopy perturbation method for nonlinear oscillator equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2581-2583.
  36. Xu, Lan, 2008. "Variational approach to solitons of nonlinear dispersive K(m,n) equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 137-143.
  37. 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.
  38. 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.
  39. 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.
  40. Al-Khaled, Kamel, 2007. "Theory and computation in singular boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 678-684.
  41. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
  42. Wu, Tzong-Mou, 2007. "The secant–homotopy continuation method," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 888-892.
  43. 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.
  44. 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.
  45. 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.
  46. 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).
  47. 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.
  48. Ghorbani, Asghar, 2009. "Beyond Adomian polynomials: He polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1486-1492.
  49. 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.
  50. 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.
  51. 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.
  52. 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.
  53. Demiray, Hilmi, 2006. "Interaction of nonlinear waves governed by Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1185-1189.
  54. 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.
  55. 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.
  56. 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).
  57. Alessandra Jannelli, 2020. "Numerical Solutions of Fractional Differential Equations Arising in Engineering Sciences," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
  58. He, Ji-Huan & Wu, Xu-Hong, 2006. "Exp-function method for nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 700-708.
  59. 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.
  60. Soliman, A.A., 2009. "Exact solutions of KdV–Burgers’ equation by Exp-function method," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 1034-1039.
  61. 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.
  62. 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.
  63. 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.
  64. 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.
  65. 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.
  66. 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.
  67. 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.
  68. 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.
  69. Moghimi, Mahdi & Hejazi, Fatemeh S.A., 2007. "Variational iteration method for solving generalized Burger–Fisher and Burger equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1756-1761.
  70. 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.
  71. 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.
  72. Chun, Changbum, 2007. "Integration using He’s homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 34(4), pages 1130-1134.
  73. Abbasbandy, S., 2007. "Application of He’s homotopy perturbation method to functional integral equations," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1243-1247.
  74. Uzar, Neslihan & Ballikaya, Sedat, 2013. "Investigation of classical and fractional Bose–Einstein condensation for harmonic potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1733-1741.
  75. Az-Zo'bi, Emad A. & Dawoud, Kamal Al & Marashdeh, Mohammad, 2015. "Numeric-analytic solutions of mixed-type systems of balance laws," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 133-143.
  76. (Benn)Wu, Xu-Hong & He, Ji-Huan, 2008. "EXP-function method and its application to nonlinear equations," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 903-910.
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