Abstract In this communication, we show that a family of partial differential equations such as the linear and nonlinear wave equations propagating in an inhomogeneous medium may be derived if the action functional is replaced by a new functional characterized by two occurrences of integrals where the integrands are non-standard singular Lagrangians. Several features are illustrated accordingly.

中文翻译：

---

非标准奇异拉格朗日函数在非均匀介质中的非线性波动方程，具有两次积分

摘要 在本次交流中，我们表明，如果作用泛函被一个以两次出现积分为特征的新泛函取代，其中被积函数为非标准奇异拉格朗日函数。相应地说明了几个特征。