Wave equation

The wave equation is a second-order linear PDE that describes the propagation of a variety of waves, such as sound waves, light waves or water waves. It arises in different fields such as acoustics, electromagnetics, and fluid dynamics. The wave equation is the example of a hyperbolic PDE. In its simplest form, the wave equation refers to a scalar function $u=u(\mathbf{r},t)$ , $\mathbf{r}\in\mathbb{R}^n$ that satisfies:

$$\frac{\partial^2 u}{\partial t^2}=c^2\nabla^2 u.$$ (2.1)

Here $\nabla^2$ denotes the Laplacian and $c$ is a constant speed of the wave propagation.