4 papers · 1 filter
Data-driven Soliton Manifold Approximations for Dark and Bright Waves: Some Prototypical 1d Case Examples
Su Yang, Shaoxuan Chen, Wei Zhu +1
In this paper, we revisit the investigation of solitary-wave interactions in the nonlinear Schrödinger model, both in the presence and absence of a parabolic trapping potential. Wh…
Quasi-continuum approximations for nonlinear dispersive waves in general discrete conservation laws
Su Yang
In this paper, we study a non-integrable discrete lattice model which is a variant of an integrable discretization of the standard Hopf equation. Interestingly, a direct numerical…
First-order continuum models for nonlinear dispersive waves in the granular crystal lattice
Su Yang, Gino Biondini, Christopher Chong +1
We derive and analyze, analytically and numerically, two first-order continuum models to approximate the nonlinear dynamics of granular crystal lattices, focusing specifically on s…
Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach
Shaoxuan Chen, Su Yang, Panayotis G. Kevrekidis +1
We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which…