Exponentially stable breather solutions in nonautonomous dissipative nonlinear Schrödinger lattices

We consider damped and forced discrete nonlinear Schr\"odinger equations on the lattice \mathbb{Z}. First we establish the existence of periodic and quasiperiodic breather solutions for periodic and quasiperiodic driving, respectively. Notably, quasiperiodic breathers cannot exist in the system without damping and driving. Afterwards the existence of a global uniform attractor... Show more