Structure-preserving reduced-order modeling of Korteweg–de Vries equation

Computationally efficient, structure-preserving reduced-order methods are developed for the Korteweg de Vries (KdV) equations in Hamiltonian form. The KdV equation is discretized space by finite differences. resulting skew-gradient system of ordinary differential (ODEs) integrated with linearly implicit Kahan's method, which preserves approximately. We have shown, using proper orthogonal decomposition (POD), structure full-order model (FOM) preserved (ROM). quadratic nonlinear terms evaluated efficiently use tensorial methods, clearly separating offline-online cost FOMs and ROMs. accuracy reduced solutions, preservation Hamiltonian, momentum mass, computational speed-up gained ROMs demonstrated one-dimensional equation, coupled two-dimensional Zakharov-Kuznetzov soliton solutions