中国物理B ›› 2002, Vol. 11 ›› Issue (6): 547-552.doi: 10.1088/1009-1963/11/6/306

• GENERAL • 上一篇    下一篇

Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential

化存才, 刘延柱   

  1. Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China
  • 收稿日期:2001-10-25 修回日期:2001-11-12 出版日期:2005-06-12 发布日期:2005-06-12
  • 基金资助:
    Project supported by the Postdoctoral Science Foundation of China (Grant No 28) and by the Shanghai Scientific and Technological Development Foundation, China (Grant No 98JC14032).

Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential

Hua Cun-Cai (化存才), Liu Yan-Zhu (刘延柱)   

  1. Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China
  • Received:2001-10-25 Revised:2001-11-12 Online:2005-06-12 Published:2005-06-12
  • Supported by:
    Project supported by the Postdoctoral Science Foundation of China (Grant No 28) and by the Shanghai Scientific and Technological Development Foundation, China (Grant No 98JC14032).

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摘要： For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV－mKdV equation.

Abstract: For the nonlinear wave equation with quartic polynomial potential, bifurcation and solitary waves are investigated. Based on the bifurcation and the energy integral of the two-dimensional dynamical system satisfied by the travelling waves, it is very interesting to find different sufficient and necessary conditions in terms of the bifurcation parameter for the existence and coexistence of bright, dark solitary waves and shock waves. The method of direct integration is developed to give all types of solitary wave solutions. Our method is simpler than other newly developed ones. Some results are similar to those obtained recently for the combined KdV－mKdV equation.

Key words: bifurcation, solitary waves, nonlinear wave equation

中图分类号:  (Solitons)

  • 05.45.Yv
02.30.Oz (Bifurcation theory) 02.30.Rz (Integral equations) 02.30.Cj (Measure and integration) 02.10.De (Algebraic structures and number theory)