Though　the　celebrated　spin　echoes　have　been　widely　used　to　reverse　quantum　dynamics,　they　are　not　applicable　to　systems　whose　constituents　are　beyond　the　control　of　the　su(2)　algebra.　Here,　we　design　echoes　to　reverse　quantum　dynamics　of　breathers　in　three-dimensional　unitary　fermions　and　two-dimensional　bosons　and　fermions　with　contact　interactions,　which　are　governed　by　an　underlying　su(1,1)　algebra.　Geometrically,　SU(1,1)　echoes　produce　closed　trajectories　on　a　single　or　multiple　Poincaré　disks　and　thus　could　recover　any　initial　states　without　changing　the　sign　of　the　Hamiltonian.　In　particular,　the　initial　shape　of　a　breather　determines　the　superposition　of　trajectories　on　multiple　Poincaré　disks　and　whether　the　revival　time　has　period　multiplication.　Our　work　provides　physicists　with　a　recipe　to　tailor　collective　excitations　of　interacting　many-body　systems.