IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v70y2015icp49-57.html
   My bibliography  Save this article

Approximate damped oscillatory solutions and error estimates for the perturbed Klein–Gordon equation

Author

Listed:
  • Ye, Caier
  • Zhang, Weiguo

Abstract

The influence of perturbation on traveling wave solutions of the perturbed Klein–Gordon equation is studied by applying the bifurcation method and qualitative theory of dynamical systems. All possible approximate damped oscillatory solutions for this equation are obtained by using undetermined coefficient method. Error estimates indicate that the approximate solutions are meaningful. The results of numerical simulations also establish our analysis.

Suggested Citation

  • Ye, Caier & Zhang, Weiguo, 2015. "Approximate damped oscillatory solutions and error estimates for the perturbed Klein–Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 70(C), pages 49-57.
    • Handle: RePEc:eee:chsofr:v:70:y:2015:i:c:p:49-57
    DOI: 10.1016/j.chaos.2014.11.003
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077914001878
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2014.11.003?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Zhang, Huiqun, 2008. "New exact travelling wave solutions for some nonlinear evolution equations, Part II," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1328-1334.
    2. Wazwaz, Abdul-Majid, 2006. "Compactons, solitons and periodic solutions for some forms of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1005-1013.
    3. Li, Bacui & Zhang, Yufeng, 2008. "Explicit and exact travelling wave solutions for Konopelchenko–Dubrovsky equation," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1202-1208.
    Full references (including those not matched with items on IDEAS)

    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. Jang, Bongsoo, 2009. "New exact travelling wave solutions of nonlinear Klein–Gordon equations," Chaos, Solitons & Fractals, Elsevier, vol. 41(2), pages 646-654.
    2. Seadawy, A.R. & El-Kalaawy, O.H. & Aldenari, R.B., 2016. "Water wave solutions of Zufiria’s higher-order Boussinesq type equations and its stability," Applied Mathematics and Computation, Elsevier, vol. 280(C), pages 57-71.
    3. Lv, Xiumei & Lai, Shaoyong & Wu, YongHong, 2009. "An auxiliary equation technique and exact solutions for a nonlinear Klein–Gordon equation," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 82-90.
    4. 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.
    5. Deng, Dingwen & Liang, Dong, 2018. "The time fourth-order compact ADI methods for solving two-dimensional nonlinear wave equations," Applied Mathematics and Computation, Elsevier, vol. 329(C), pages 188-209.
    6. Md. Asaduzzaman & Adem Kilicman & Md. Zulfikar Ali & Siti Hasana Sapar, 2020. "Fixed Point Theorem Based Solvability of 2-Dimensional Dissipative Cubic Nonlinear Klein-Gordon Equation," Mathematics, MDPI, vol. 8(7), pages 1-12, July.
    7. Sivenathi Oscar Mbusi & Ben Muatjetjeja & Abdullahi Rashid Adem, 2021. "Lagrangian Formulation, Conservation Laws, Travelling Wave Solutions: A Generalized Benney-Luke Equation," Mathematics, MDPI, vol. 9(13), pages 1-6, June.
    8. Belmonte-Beitia, Juan & Pérez-García, Víctor M. & Vekslerchik, Vadym, 2007. "Modulational instability, solitons and periodic waves in a model of quantum degenerate boson–fermion mixtures," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1268-1277.
    9. Nur Alam & Fethi Bin Muhammad Belgacem, 2016. "Microtubules Nonlinear Models Dynamics Investigations through the exp(−Φ(ξ))-Expansion Method Implementation," Mathematics, MDPI, vol. 4(1), pages 1-13, February.
    10. Bekir, Ahmet, 2009. "The tanh–coth method combined with the Riccati equation for solving non-linear equation," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1467-1474.

    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:eee:chsofr:v:70:y:2015:i:c:p:49-57. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.