Bifurcations of Solitary Wave Solutions to the Shallow Water Equation of Moderate Amplitude
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摘要: 利用平面动力系统分支方法研究浅水中度振幅方程的定性行为和孤立波解.给出了系统在不同参数条件下的相图.获得了光滑孤立波、cuspon解和周期波解的隐式表达式.对方程的光滑孤立波解、cuspon解和周期波解进行了数值模拟.获得的结果完善了相关文献已有的结果.Abstract: The qualitative behavior and solitary wave solutions to the model equation for shallow water waves of moderate amplitude were studied with the bifurcation method for dynamic systems. The phase portraits of the system were given under different parametric conditions. The implicit expressions of the smooth solitary waves, cuspons and periodic wave solutions were obtained. Numerical simulations were conducted for the smooth solitary waves, cuspons and periodic wave solutions to the model equation. The results show that the presented findings improve the related previous conclusions.
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Key words:
- solitary wave /
- cuspon wave /
- periodic wave /
- bifurcation
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