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Bifurcation Phenomena of Nonlinear Waves in a Generalized Zakharov‐Kuznetsov Equation

Author

Listed:
  • Yun Wu
  • Zhengrong Liu

Abstract

We study the bifurcation phenomena of nonlinear waves described by a generalized Zakharov‐Kuznetsov equation ut + (au2 + bu4)ux + γuxxx + δuxyy = 0. We reveal four kinds of interesting bifurcation phenomena. The first kind is that the low‐kink waves can be bifurcated from the symmetric solitary waves, the 1‐blow‐up waves, the tall‐kink waves, and the antisymmetric solitary waves. The second kind is that the 1‐blow‐up waves can be bifurcated from the periodic‐blow‐up waves, the symmetric solitary waves, and the 2‐blow‐up waves. The third kind is that the periodic‐blow‐up waves can be bifurcated from the symmetric periodic waves. The fourth kind is that the tall‐kink waves can be bifurcated from the symmetric periodic waves.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlamp:v:2013:y:2013:i:1:n:812120
    DOI: 10.1155/2013/812120
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    References listed on IDEAS

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    1. Shaoyong Li & Rui Liu, 2013. "Some Explicit Expressions and Interesting Bifurcation Phenomena for Nonlinear Waves in Generalized Zakharov Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-19, May.
    2. Ming Song, 2012. "Application of Bifurcation Method to the Generalized Zakharov Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, November.
    3. Ming Song, 2012. "Application of Bifurcation Method to the Generalized Zakharov Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Shaoyong Li & Rui Liu, 2013. "Some Explicit Expressions and Interesting Bifurcation Phenomena for Nonlinear Waves in Generalized Zakharov Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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