In the one-dimensional space a conservation equation is a first-order quasilinear hyperbolic equation that can be put into the advection form: y t + a ( y ) y x = 0 where the dependent variable y (x, t) is called the density of the conserved (scalar) quantity, and a (y) is called the current coefficient, usually corresponding to the partial derivative in the conserved quantity of a current density of the conserved quantity j (y) : a ( y ) = j y ( y )