The project aims at developing the Riemann-Hilbert (RH) approach to the construction of periodic finite-band solutions to nonlinear integrable partial differential equations. In particular, we are going to deal with two types of equations: (i) the Short Pulse (SP) Equation and its generalizations, including complex versions; (ii) multicomponent equations like the Manakov system. The study is motivated by the fact that equations of both types can be used for modeling nonlinear wave propagation in fiber-optic links: the SP equation is relevant when modeling the propagation of ultra-short pulses where the width of optical pulse is in order of femtosecond whereas multicomponent systems involve the polarization-related degrees of freedom that can be used for improving (doubling) the system’s throughput. Solving periodic problems for the relevant partial differential equations corresponds to considering periodically continued signals whose processing has important advantages compared with conventional nonlinear Fourier transform algorithms. Our approach to these problems is based on the Fokas method for initial boundary value problems for nonlinear equations, at the core of which is the construction of an associated Riemann-Hilbert factorization problem formulated in the complex plane of the spectral parameter (a nonlinear version of the Fourier transform method). Building on this method, a finite-band solution to the corresponding nonlinear equation can be given in terms of the solution of the RH problem, the jump conditions for which are characterized by specifying the endpoints of the arcs defining the contour of the RH problem and the constants (so-called phases) involved in the jump matrices. In particular, we are going to solve the problem of retrieving the phases given the solution of the corresponding nonlinear partial differential equations evaluated at a fixed time, which is associated with the problem of decoding of received signals.