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Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d‐Sokolov System

Author

Listed:
  • Huixian Cai
  • Chaohong Pan
  • Zhengrong Liu

Abstract

We study the bifurcations of nonlinear waves for the generalized Drinfel’d‐Sokolov system ut+(vm)x=00,vt+a(vn)xxx+buxv+cuvx= called D(m, n) system. We reveal some interesting bifurcation phenomena as follows. (1) For D(2, 1) system, the fractional solitary waves can be bifurcated from the trigonometric periodic waves and the elliptic periodic waves, and the kink waves can be bifurcated from the solitary waves and the singular waves. (2) For D(1, 2) system, the compactons can be bifurcated from the solitary waves, and the peakons can be bifurcated from the solitary waves and the singular cusp waves. (3) For D(2, 2) system, the solitary waves can be bifurcated from the smooth periodic waves and the singular periodic waves.

Suggested Citation

  • Huixian Cai & Chaohong Pan & Zhengrong Liu, 2014. "Some Interesting Bifurcations of Nonlinear Waves for the Generalized Drinfel’d‐Sokolov System," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:189486
    DOI: 10.1155/2014/189486
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    References listed on IDEAS

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    1. Fu Zhang & Jian-ming Qi & Wen-jun Yuan, 2013. "Further Results about Traveling Wave Exact Solutions of the Drinfeld-Sokolov Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-6, October.
    2. Fu Zhang & Jian-ming Qi & Wen-jun Yuan, 2013. "Further Results about Traveling Wave Exact Solutions of the Drinfeld‐Sokolov Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
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