On the solution for the initial-boundary value problem for a nonlocal elliptic–hyperbolic system related to the short pulse equation

In this paper, we consider a non-local elliptic-hyperbolic system related to short pulse equation. That equation describes the dynamics of the electrical field of linearly polarized continuum spectrum pulses in optical waveguides, including fused-silica telecommunication-type or photonic-crystal fibers, as well as hollow capillaries filled with transparent gases or liquids. We augment the equations with some boundary conditions and prove the well-posedness of the global in time distributional solution.