Transient wave propagation in a waveguide filled with an inhomogeneous dispersive medium is analyzed. The waveguide is inhomogeneous in the longitudinal direction, but is homogeneously filled in the transverse directions. The analysis is performed in the time domain and is based upon a wave splitting technique and the method of propagators. The propagator maps the exciting field from one position in the waveguide to the field at another position. This mapping is represented as time convolution integrals. The theory is exemplified by numerical examples where it is shown how wave trains of different shapes are propagating in a waveguide filled with a homogeneous dispersive medium.
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