Periodic structures described by the perturbed Burgers–Korteweg–de Vries equation

• The perturbed Burgers–Korteweg–de Vries equation.
• Classical and non-classical symmetries.
• Periodic and solitary wave structures.

We study the perturbed Burgers–Korteweg–de Vries equation. This equation can be used for the description of non-linear waves in a liquid with gas bubbles and for the description of non-linear waves on a fluid layer flowing down an inclined plane. We investigate the integrability of this equation using the Painlevé approach. We show that the perturbed Burgers–Korteweg–de Vries equation does not belong to the class of integrable equations. Classical and non-classical symmetries admitted by this equation and corresponding symmetry reductions are constructed. New types of periodic analytical structures described by the Burgers–Korteweg–de Vries equation are found.