We examine the effects of discreteness on a prototypical example of a collapse exhibiting partial differential equation (PDE). As our benchmark example, we select the discrete nonlinear Schrödinger (DNLS) equation. We provide a number of physical settings where issues of the interplay of...

In this paper we investigate the emergence of time-periodic and time quasiperiodic (sometimes infinitely long-lived and sometimes very long-lived or metastable) solutions of discrete nonlinear wave equations: discrete sine Gordon, discrete φ4 and discrete nonlinear Schrödinger equation (DNLS)....

We demonstrate the systematic derivation of a class of discretizations of nonlinear Schrödinger (NLS) equations for general polynomial nonlinearity whose stationary solutions can be found from a reduced two-point algebraic condition. We then focus on the cubic problem and illustrate how our...