The waveguide has a perfectly conducting surface. Its cross section domain is bounded by a singly-connected contour of a rather arbitrary but enough smooth form. Possible waveguide losses are modeled by a homogeneous conductive medium in the waveguide. The boundary-value problem for the system of Maxwell's equations with time derivative is solved in the time domain. The real-valued solutions are obtained in Hilbert space L2 in a form of transverse-longitudinal decompositions. Every field component is a product of the vector element of the modal basis dependent on transverse coordinates, and the modal amplitudes dependent on time and the axial coordinate. Three examples are included. The dynamic properties of the modal waves and concomitant energetic waves are studied and their dependence on time illustrated graphically.
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