Time-periodic solutions to the Ginzburg-Landau-BBM equations (Q2745435)

The paper deals with the Ginzburg-Landau equation coupled with the BBM equation with \(\omega\)-periodic conditions. Using a priori estimates combined with the Leray-Schauder fixed point theorem the authors establish the existence and uniqueness of time-periodic solutions. There are also used standard compactness arguments to get the convergence of the approximate solutions. The problem studied in the present paper describes the nonlinear interactions between the Langmuir wave and the ion acoustic wave in plasma physics.