一类非线性四阶方程的纽结波解(英文)

The kink waves of a nonlinear quartic equation

用微分方程定性理论结合数值模拟方法研究了一类非线性四阶波动方程的纽结波.在r<0的条件下,首先把波动方程转换成一个常微平面系统,然后用定性理论讨论该平面系统的奇点性质,画出该系统的相图分支,根据相图找到了纽结波的存在条件,并求出了纽结波的解.最后用数学软件Maple对行波方程进行数值模拟,得到纽结波的平面模拟图.数值模拟进一步验证了理论分析结果.

The qualitative theory of ordinary differential equations and numerical simulation method are employed to investigate the kink waves of a nonlinear quartic equation.Under the condition r < 0,the wave equation is changed to a planar system,the properties of the singular points are studied,and the bifurcation phase portraits are drawn.The parameter conditions that the kink waves appear are found,and their solutions are obtained.Finally,the planar graphs of the traveling wave equation are simulated by using mathematical software MAPLE.The numerical simulation and qualitative results are identical.