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

In this paper, we analyze the transverse instability of periodic standing wave solutions to the generalized Schrödinger equation with a fractional power nonlinearity. The existence of periodic waves is established via a constrained minimization problem in the complex setting, and it is shown that the corresponding real-valued solution, depending on the power of the nonlinearity, is either strictly positive or sign-changing. The transverse instability results are then obtained by applying the main result from [6] in the periodic setting.