Orbital stability of periodic traveling waves to some coupled BBM equations

In this work, we show some results concerning the orbital stability of dnoidal wave solutions to some Benjamin-Bona-Mahony equations (BBM equations henceforth). First, by the standard argument, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type. Then, we show that this type of solutions are orbitally stable by perturbations with the same period L. The major tools to obtain these results are the Grillaks, Shatah and Strauss' general theory in the periodic case. The results in the present paper extend some previous stability results for the BBM equations.