Existence and congruence of global attractors for damped and forced integrable and nonintegrable discrete nonlinear Schrödinger equations

We study two damped and forced discrete nonlinear Schr\"odinger equations on the one-dimensional infinite lattice. Without damping and forcing they are represented by the integrable Ablowitz-Ladik equation (AL) featuring non-local cubic nonlinear terms, and its standard (nonintegrable) counterpart with local cubic nonlinear terms (DNLS). The global existence of a unique... Show more