Nonlinear wave equation in an inhomogeneous medium from non-standard singular Lagrangians functional with two occurrences of integrals

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.