  A reduced-order model algorithm, called ALP, is proposed to solve nonlinear
evolution partial differential equations. It is based on approximations of
generalized Lax pairs. Contrary to other reduced-order methods, like Proper
Orthogonal Decomposition, the basis on which the solution is searched for
evolves in time according to a dynamics specific to the problem. It is
therefore well-suited to solving problems with progressive front or wave
propagation. Another difference with other reduced-order methods is that it is
not based on an off-line / on-line strategy. Numerical examples are shown for
the linear advection, KdV and FKPP equations, in one and two dimensions.
