A stability analysis of periodic solutions to the steady forced Korteweg–de Vries–Burgers equation

• Using Floquet theory, two stability criteria are found for a steady generalised KdV-type equation.
• These criteria are related to the steady fKdVB equation to highlight the stability of certain periodic solutions.
• As a result, a stability threshold in terms of the coefficient of Burgers damping is found.
• A numerical analysis of the steady fKdVB equation validates these results and reveals beating solutions.

The stability of periodic solutions to the steady forced Korteweg–de Vries–Burgers (fKdVB) equation is investigated here. This family of periodic solutions was identified by Hattam and Clarke (2015) using a multi-scale perturbation technique. Here, Floquet theory is applied to the governing equation. Consequently, two criteria are found that determine when the periodic solutions are stable. This analysis is then confirmed by a numerical study of the steady fKdVB equation.