证明了具周期系数的边值问题正时间周期解的存在性以及对应初边值问题解的渐近性。

The time periodic solution problem of damped generalized coupled nonlinear wave equations with periodic boundary condition was studied.

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运用分歧理论、固有值的解析摄动理论和渐近展开的方法，获得了共存时间周期解的存在性和稳定性。

The existence and stability of periodic solution are studied by using the bifurcation theory, linear stability theory and the method of asymptotic expansion.

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此外，本文还进一步对时间周期解作了稳定性分析。结果表明，无论是在浓缩过程中还是在稀释过程中，其时间周期解都是稳定的。

And the stability analysis further shows that the time periodic solutions both in the course of concentration and in the course of dilution are stable.

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