A coaxial warp drive was a propulsion system hypothesized by Starfleet engineers in the 24th century, with the theoretic capability of folding the fabric of space, allowing a ship to travel instantaneously across extremely large distances.
Such a propulsion system was encountered in the Delta Quadrant by the crew of the USS Voyager in 2374, when they came across a ship piloted by a Benthan named Steth. Emerging from coaxial space in an unstable condition, the vessel threatened to explode and collapse space within a radius of a billion kilometers. Such a catastrophe was averted, however, when Tom Paris, Voyager's helmsman, managed to generate a symmetric warp field around Steth's ship, containing the instabilities in the space-folding core.
The coaxial induction drive functioned by drawing in subatomic particles and reconfiguring their internal geometries. The drive was imperfect, however, as particle instabilities tended to overload the engines. To correct for this flaw, Paris conceived of the idea of using a polaric modulator to dilute the particle stream as it entered the coaxial core, drawing inspiration from a 20th century device known as a carburetor.
The Voyager crew eventually discovered that Steth was, in fact, an imposter who has the literal ability to switch his DNA with another individual, in essence switching bodies. When this lifeform switched places with Captain Janeway, he attempted to escape from Voyager using a shuttle which had been modified with coaxial warp drive. Paris was able to prevent his escape, however, by targeting the polaric modulator with a chromoelectric pulse, disrupting his engines. Voyager's doctor was subsequently able to restore Paris and Janeway to their original bodies. (VOY: "Vis à Vis")