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.
Received: 25 October 2001
Revised: 12 November 2001
Accepted manuscript online:
Fund: 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).
Cite this article:
Hua Cun-Cai (化存才), Liu Yan-Zhu (刘延柱) Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential 2002 Chinese Physics 11 547
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