Integral equations for electromagnetic field in time-varying dielectric waveguide

The Volterra integral equations in time domain that are described electromagnetic fields in a longitudinal uniform waveguide are obtained. The waveguide can has an arbitrary time-varying medium in a core as well as a dissipative dielectric in a cladding. Solutions to these equations are given by resolvent operators have been constructed. These resolvent operators have allowed considering the transformation of an eigenwave caused by a time jump changing of the permittivity in the waveguide core. An appearance of the new features in transients in comparison with an unbounded space is shown.