Reduced-Order Modeling based on Approximated Lax Pairs
  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. 
Jean-Fr\'ed\'eric Gerbeau (INRIA Rocquencourt), Damiano Lombardi   (INRIA Rocquencourt)
math.NA