IDEAS home Printed from https://ideas.repec.org/a/wly/jnlaaa/v2014y2014i1n309420.html

Application of the Homotopy Analysis Method for Solving the Variable Coefficient KdV‐Burgers Equation

Author

Listed:
  • Dianchen Lu
  • Jie Liu

Abstract

The homotopy analysis method is applied to solve the variable coefficient KdV‐Burgers equation. With the aid of generalized elliptic method and Fourier’s transform method, the approximate solutions of double periodic form are obtained. These solutions may be degenerated into the approximate solutions of hyperbolic function form and the approximate solutions of trigonometric function form in the limit cases. The results indicate that this method is efficient for the nonlinear models with the dissipative terms and variable coefficients.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:309420
    DOI: 10.1155/2014/309420
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2014/309420
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2014/309420?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Zeeshan Ali & Shayan Naseri Nia & Faranak Rabiei & Kamal Shah & Ming Kwang Tan, 2021. "A Semianalytical Approach to the Solution of Time‐Fractional Navier‐Stokes Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2021(1).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ramos, J.I., 2009. "Piecewise-adaptive decomposition methods," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1623-1636.
    2. 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).
    3. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    4. 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.
    5. 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).
    6. 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).
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. Demiray, Hilmi, 2006. "Interaction of nonlinear waves governed by Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1185-1189.
    12. Tajvidi, T. & Razzaghi, M. & Dehghan, M., 2008. "Modified rational Legendre approach to laminar viscous flow over a semi-infinite flat plate," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 59-66.
    13. 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.
    14. 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.
    15. 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).
    16. Héctor Vázquez-Leal, 2012. "Rational Homotopy Perturbation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    17. 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.
    18. 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).
    19. Jules Sadefo-Kamdem, 2011. "Integral Transforms With The Homotopy Perturbation Method And Some Applications," Working Papers hal-00580023, HAL.
    20. Al-Khaled, Kamel, 2007. "Theory and computation in singular boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 678-684.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:309420. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4058 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.