Spatiotemporal wave-train instabilities in nonlinear Schrodinger equation: revisited

A complete description of properties of the wave-train bifurcating from unstable basic oscillatory states (CW nonlinear stationary states) of the nonlinear Schrödinger equation are studied in the moving frames of reference as an initial value problem and using the methods of absolute and convective instabilities. The predictions are in excellent agreement with numerical solutions and may contribute understanding the nonlinear Schrödinger equation complex dynamics under various initial conditions including, localized and/or noisy initial conditions