We show how periodic wave trains are generated in liquid layers when the liquid is heated from above or when a surface-active vapor is absorbed at a liquid of higher surface tension, Traveling periodic wave trains are excited beyond a critical Marangoni number. In heat-transfer experiments the critical Marangoni number is of the order of 10(5). We present examples of wave patterns in square and annular containers. The synchronization results from resonance of the waves with the finite size of the containers and from wave interaction. During reflections at the walls and during collisions with each other the wave crests undergo nonlinear interactions. They recover their velocity and their identity shortly after these interactions. Depending on the angle of collision, we observe a negative or positive phase-shift at moderate supercritical Marangoni numbers, which is a typical feature of solitonic waves. This behavior has been observed in both heat-transfer and mass-transfer experiments.