Transverse instability of periodic standing waves for the generalized nonlinear Schrodinger equation

Abstract: In this paper, we determine the transverse instability of periodic standing wave solutions for the generalized Schr\"odinger equation with fractional power nonlinearity. The existence of periodic waves is determined by using a constrained minimization problem in the complex setting, and it is shown that the corresponding real solution, depending on the power nonlinearity, is always positive or changes its sign. The transverse instability results are then determined by applying the main result given in \cite{RoussetTzvetkov} for the periodic case.