An impulsive wave is a good example of transient waves and often serves as a good start in transient wave study. Somehow since 20th century, most study in wave behaviours focused on the harmonic side, partly because the theory of Fourier transformation lent a powerful arm to harmonic analysis. Transient wave behaviours are often regarded as more difficult to study theoretically and are often evaded in discussion. Yet they are of extreme practical importance. Seismic waves, for example, are transient by nature.
Most waves used in radar, sonar, and ultrasonic technologies, are also transient.
While it is not totally untrue that transient solutions are sometimes more difficult to obtain, they are not necessarily more complicated, as is examplified in my study. Clearer physical pictures can often be drawn from transient solutions. Head waves and lacunas, for example, are best examined in a transient regime. Understandably, anisotropy creates special difficulties in wave analysis. In particular, it is often difficult to obtain exact solutions in the case of general anisotropy.