Analytic solutions are presented to the non-paraxial wave equation
describing an ultra-short, low-power, laser pulse propagating in a
plasma channel. Expressions for the laser pulse centroid motion and
laser group velocity are derived, valid for matched and mismatched
propagation in a parabolic plasma channel, as well as in vacuum, for
an arbitrary Laguerre-Gaussian laser mode. The group velocity of a
mismatched laser pulse, for which the laser spot size is strongly
oscillating, is found to be independent of propagation distance and
significantly less than that of a matched pulse. Laser pulse
lengthening of a mismatched pulse owing to laser mode slippage is
examined and found to dominate over that due to dispersive pulse
spreading for sufficiently long pulses. Analytic results are shown to
be in excellent agreement with numerical solutions of the full Maxwell
equations coupled to the plasma response. Implications for plasma
channel diagnostics are discussed.