摘要
本文考虑广义Camassa-Holm方程。采用微分方程定性分析、动力系统分支、相平面分析、精确计算、微分方程数值模拟等相结合的办法,对该方程的有界行波进行比较系统研究,得到关于定常态的奇点类型和分支解等。用计算机绘出了所得函数的图形,同时也从方程本身出发,模拟出了有界波的平面图,理论结果和数值模拟互相验证了其正确性。
We consider in this paper the generalized Camassa-Holm equation, whose bounded traveling waves axe studied by using qualitative analysis of differential equations, bifurcation of dynamical systems, phase plane analysis, accurate integration and numerical simulation of differential equations. The types of singularity of steady solutions and distribution of solution branches are determined. The graphs of the explicit or implicit functions are drawn. The planar graphs of the bounded waves are also simulated. The theoretical results and numerical results are testified each other.
出处
《工程数学学报》
CSCD
北大核心
2006年第3期381-398,共18页
Chinese Journal of Engineering Mathematics
