Twisted localized modes

In a number of recent papers the so-called twisted localized mode of the discrete nonlinear Schrödinger equation has been proposed. Herein, we study the existence and stability properties of such modes. We analyze the persistence of quasiperiodic modes and study the domains of existence and numerical stability of the exact form of such solutions. We identify the bifurcations through which they lose their stability and follow the behavior of the intrinsic localized modes and their eigenmodes even in the unstable regime.