  We study the propagation of three-dimensional bipolar ultrashort
electromagnetic pulses in an array of semiconductor carbon nanotubes at times
much longer than the pulse duration, yet still shorter than the relaxation time
in the system. The interaction of the electromagnetic field with the electronic
subsystem of the medium is described by means of Maxwell's equations, taking
into account the field inhomogeneity along the nanotube axis beyond the
approximation of slowly varying amplitudes and phases. A model is proposed for
the analysis of the dynamics of an electromagnetic pulse in the form of an
effective equation for the vector potential of the field. Our numerical
analysis demonstrates the possibility of a satisfactory description of the
evolution of the pulse field at large times by means of a three-dimensional
generalization of the sine-Gordon and double sine-Gordon equations.
