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Topological Soliton Solution and Bifurcation Analysis of the Klein‐Gordon‐Zakharov Equation in (1 + 1)‐Dimensions with Power Law Nonlinearity

Author

Listed:
  • Ming Song
  • Bouthina S. Ahmed
  • Anjan Biswas

Abstract

This paper addresses the Klein‐Gordon‐Zakharov equation with power law nonlinearity in (1 + 1)‐dimensions. The integrability aspect as well as the bifurcation analysis is studied in this paper. The numerical simulations are also given where the finite difference approach was utilized. There are a few constraint conditions that naturally evolve during the course of derivation of the soliton solutions. These constraint conditions must remain valid in order for the soliton solution to exist. For the bifurcation analysis, the phase portraits are also given.

Suggested Citation

  • Ming Song & Bouthina S. Ahmed & Anjan Biswas, 2013. "Topological Soliton Solution and Bifurcation Analysis of the Klein‐Gordon‐Zakharov Equation in (1 + 1)‐Dimensions with Power Law Nonlinearity," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:972416
    DOI: 10.1155/2013/972416
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    References listed on IDEAS

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    1. Ming Song & Zhengrong Liu, 2012. "Periodic Wave Solutions and Their Limits for the Generalized KP‐BBM Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Ming Song & Zhengrong Liu, 2012. "Periodic Wave Solutions and Their Limits for the Generalized KP-BBM Equation," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-25, July.
    3. Ming Song, 2012. "Application of Bifurcation Method to the Generalized Zakharov Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, November.
    4. Ming Song, 2012. "Application of Bifurcation Method to the Generalized Zakharov Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. Li, Jibin, 2007. "Exact explicit travelling wave solutions for (n+1)-dimensional Klein–Gordon–Zakharov equations," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 867-871.
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    Cited by:

    1. Zhenshu Wen, 2014. "New Exact Explicit Nonlinear Wave Solutions for the Broer‐Kaup Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Ben-gong Zhang, 2013. "Analytical and Multishaped Solitary Wave Solutions for Extended Reduced Ostrovsky Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    3. Yating Yi & Zhengrong Liu, 2013. "The Bifurcations of Traveling Wave Solutions of the Kundu Equation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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