Reduced-Order Modeling based on Approximated Lax Pairs
For researchers solving nonlinear PDEs with traveling waves, this method offers a dynamics-adapted basis that outperforms static basis methods like POD.
The paper proposes a reduced-order modeling algorithm based on approximated Lax pairs for solving nonlinear evolution PDEs, demonstrating effectiveness on KdV and FKPP equations with progressive waves and front propagation.
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.