Shape-morphing reduced-order models for nonlinear Schrödinger equations

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