中文摘要：

针对一类非线性波方程的局部临界周期分支问题,借用计算机代数系统 Mathematica,计算对应平面微分自治系统的周期常数,得到平面自治系统原点成为一阶细中心的充要条件,并证明该系统在原点邻域存在1个局部临界周期分支。结果表明,该非线性波方程恰有1个局部临界周期分支。

英文摘要：

The local bifurcation of critical period problem for a nonlinear wave equation is discussed.Using the computer alge-bra system Mathematica,the period constants for the corresponding planar autonomous differential system are calculated. The necessary and sufficient condition for the origin to be one order weak center is obtained.It is proved that there is one lo-cal critical period bifurcation in the origin of the system.The result shows that the nonlinear wave equation has one local bi-furcation of critical period.