Breathers in a nonautonomous Toda lattice with pulsating coupling

We study a nonautonomous Toda lattice, with a periodically switched on-off coupling coefficient, describing a pulsating strength of neighbor particle interaction. It is shown that when the uncoupled oscillations are linear and under appropriate conditions for the duration of the time intervals where the coupling is switched off, breather solutions can be obtained analytically. Their dynamics and collisions are related to the soliton dynamics of the corresponding autonomous Toda lattice, while a ratchet effect is shown to result in breather deceleration, providing a mechanism for breather velocity and collision control.