Let us now see how the Maxwell equations (17.2)–(17.5) predict the existence of electromagnetic waves. For simplicity we will consider a region of space and time in which there are no sources (i.e., we consider the propagation of electromagnetic waves in vacuum). Thus we set p = 0 = j in our space-time region of interest. Now all the Maxwell equations are linear, homogeneous.
maxwell equation, space, time, electromagnetic, chapter 18
Physical Sciences and Mathematics | Physics
Torre, Charles G., "18 The Electromagnetic Wave Equation" (2014). Foundations of Wave Phenomena. Book 5.