  A reduced-order model algorithm, based on approximations of Lax pairs, is
proposed to solve nonlinear evolution partial differential equations. Contrary
to other reduced-order methods, like Proper Orthogonal Decomposition, the space
where the solution is searched for evolves according to a dynamics specific to
the problem. It is therefore well-suited to solving problems with progressive
waves or front propagation. Numerical examples are shown for the KdV and FKPP
(nonlinear reaction diffusion) equations, in one and two dimensions.
