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...

We examine how nonlinear dispersion relations (NLDR) can be used as a simple, universal algebraic tool to provide information for the localized, nonlinear solutions of PDE that model physical systems. Such scaling relations between width, amplitude and velocity are of great help for numerical...