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The present paper deals to the quintom model of dark energy. We introduce afirst-order formalism, which shows how to relate the potential that specifiesthe scalar field model to Hubble parameter. Reviewing briefly the quintomscenario of dark energy, we present a general procedure to solve the equationsof motion for quintom model driven by a couple scalar fields with first-orderdifferential equations.

First-order formalism for the quintom model of dark energy