  We discuss the Lugiato-Lefever equation and its variant with third-order
dispersion, which are mathematical models used to describe how a light beam
forms patterns within an optical cavity. It is mathematically demonstrated that
the solutions of these equations follow the Talbot effect, which is a
phenomenon of periodic self-imaging of an object under certain conditions of
diffraction. The Talbot effect is regarded as the underlying cause of pattern
formation in optical cavities.
