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

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    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.
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