CAJ | 학술논문

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.
용미분방정정성이론결합수치모의방법연구료일류비선성사계파동방정적뉴결파. 재r＜ 0적조건하,수선파파동방정전환성일개상미평면계통,연후용정성이론토론해평면계통적기점성질,화출해계통적상도분지,근거상도조도료뉴결파적존재조건,병구출료뉴결파적해. 최후용수학연건Maple대행파방정진행수치모의,득도뉴결파적평면모의도. 수치모의진일보험증료이론분석결과.
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.