2022 article

Shape-morphing reduced-order models for nonlinear Schrodinger equations

Anderson, W., & Farazmand, M. (2022, April 25). NONLINEAR DYNAMICS.

By: W. Anderson n & M. Farazmand n 

co-author countries: United States of America πŸ‡ΊπŸ‡Έ
author keywords: Model order reduction; Partial differential equations; Nonlinear Schrodinger equation; Variational methods
Source: Web Of Science
Added: May 10, 2022

We consider reduced-order modeling of nonlinear dispersive waves described by a class of nonlinear Schrodinger (NLS) equations. We compare two nonlinear reduced-order modeling methods: (i) The reduced Lagrangian approach which relies on the variational formulation of NLS and (ii) The recently developed method of reduced-order nonlinear solutions (RONS). First, we prove the surprising result that, although the two methods are seemingly quite different, they can be obtained from the real and imaginary parts of a single complex-valued master equation. Furthermore, for the NLS equation in a stationary frame, we show that the reduced Lagrangian method fails to predict the correct group velocity of the waves whereas RONS predicts the correct group velocity. Finally, for the modified NLS equation, where the reduced Lagrangian approach is inapplicable, the RONS reduced-order model accurately approximates the true solutions.