| Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential |
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| 作者姓名： | 化存才 刘延柱 |
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| 作者单位： | Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China;Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China |
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| 基金项目： | 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.
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| 关 键 词： | 非线性波动方程 四阶多项式势函数 孤子波 分叉波 |
| 收稿时间： | 2001-10-25 |
Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential |
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| Hua Cun-Cai and Liu Yan-Zhu.Bifurcation and solitary waves of the nonlinear wave equation with quartic polynomial potential[J].Chinese Physics B,2002,11(6):547-552. |
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| Authors: | Hua Cun-Cai and Liu Yan-Zhu |
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| Institution: | Department of Engineering Mechanics, Shanghai Jiaotong University, Shanghai 200030, China |
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| 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. |
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| Keywords: | bifurcation solitary waves nonlinear wave equation |
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