【摘要】 用微分方程分支理论和计算机数值模拟方法研究广义CH方程的周期波解.给出了行波系统的分支相图,利用相图的周期轨构造出了周期波解,在数学软件M ap le支持下用计算机进行数值模拟,发现了周期波的两种极限情况,第一种情况是光滑周期波趋于周期尖波,第二种情况是光滑周期波趋于光滑孤立波.这些结果丰富了广义CH方程的研究内容.更多还原

【Abstract】 The periodic wave solutions of the generalized CH equation are investi gated by using bifurcation theory of differential equations and numerical simulations.The bifurcation phase portraits of traveling system are given.The periodic wave solutions are constructed by using the periodic orbits of phase portraits.The numerical simulations are run in the software Maple.Two limited cases of the periodic wave are discovered.In the first case,the smooth periodic wave tends to the periodic cusp wave.In the second case,the smooth periodic wave tends to the smooth solitary wave.These results enrich the research in contents of the generalized CH equation.更多还原