【摘要】 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Boussinesq方程的有界行波.在r>0的条件下,首先把Boussinesq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,得到了该系统的相图分支,根据相图给出了有界行波的存在条件,并求出了有界行波的解.最后用数学软件Maple对行波方程进行数值模拟,得到了有界行波的平面模拟图.数值模拟和理论分析结果是一致的.更多还原

【Abstract】 The qualitative theory of ordinary differential equations and numerical simulation method are employed to investigate the bounded traveling waves of a nonlinear Boussinesq equation.Under the condition r>0,the Boussinesq equation is changed to a planar system,the proprties of the singular points are studied and the bifurcation phase portraits are drew.The parameter conditions that the bounded traveling waves appear are found,and their solutions are obtained.Finally,the planar graphs of the traveling wave equation are simulated by use mathematical software Maple.The numerical simulation and qualitative results are identical.更多还原