Approximated Lax Pairs for the Reduced Order Integration of Nonlinear   Evolution Equations
  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. 
Jean-Fr\'ed\'eric Gerbeau (INRIA Paris-Rocquencourt), Damiano Lombardi   (INRIA Paris-Rocquencourt)
math.NA