Theoretical calculations predict that by coupling an exothermic chemical reaction with a nanotube or nanowire possessing a high axial thermal conductivity, a self-propagating reactive wave can be driven along its length. Herein, such waves are realized using a 7-nm cyclotrimethylene trinitramine annular shell around a multiwalled carbon nanotube and are amplified by more than 10⁴ times the bulk value, propagating faster than 2 m s⁻¹, with an effective thermal conductivity of 1.28±0.2 kW m⁻¹ K⁻¹ at 2,860 K. This wave produces a concomitant electrical pulse of disproportionately high specific power, as large as 7 kW kg⁻¹, which we identify as a thermopower wave. Thermally excited carriers flow in the direction of the propagating reaction with a specific power that scales inversely with system size. The reaction also evolves an anisotropic pressure wave of high total impulse per mass (300 N s kg⁻¹). Such waves of high power density may find uses as unique energy sources.