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Application of Bifurcation Method to the Generalized Zakharov Equations

Author

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  • Ming Song

Abstract

We use the bifurcation method of dynamical systems to study the traveling wave solutions for the generalized Zakharov equations. A number of traveling wave solutions are obtained. Those solutions contain explicit periodic blow-up wave solutions and solitary wave solutions.

Suggested Citation

  • Ming Song, 2012. "Application of Bifurcation Method to the Generalized Zakharov Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, November.
    • Handle: RePEc:hin:jnlaaa:308326
    DOI: 10.1155/2012/308326
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    Cited by:

    1. Yun Wu & Zhengrong Liu, 2013. "Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov‐Kuznetsov Equation," Advances in Mathematical Physics, John Wiley & Sons, vol. 2013(1).
    2. 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).
    3. 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).
    4. Yun Wu & Zhengrong Liu, 2013. "New Types of Nonlinear Waves and Bifurcation Phenomena in Schamel‐Korteweg‐de Vries Equation," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. Song, Ming & Liu, Zhengrong, 2014. "Periodic wave solutions and their limits for the ZK–BBM equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 9-26.
    6. Pradhan, Dickcha & Ali, Khalid K. & Karakoc, Seydi Battal Gazi & Saha, Asit, 2026. "New families of soliton solutions and dynamics of nonlinear traveling waves for the Whitham–Broer–Kaup equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 239(C), pages 376-390.

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