Learning effective soliton dynamics from scattering data using weak-form system identification
Year: 2026
Type: article
Abstract: The inverse scattering transform (IST) provides the standard theoretical framework for deriving soliton dynamics. Traditionally, such derivations have been of an analytical, rather than data-driven, nature. In this paper, we combine the conceptual framework of the IST with weak-form system identification methods to discover effective soliton dynamics directly from observed scattering data, without assuming prior knowledge of the scattering equations. Our method avoids parameterizing solitary waves via ad hoc curve-fitting by working in the scattering domain, yielding interpretable low-dimensional models that remain valid in perturbed and near-integrable regimes. We demonstrate the performance of the proposed approach on synthetic and experimental data governed by shallow-water equations of Korteweg–de Vries-type and recover models that are consistent with canonical IST theory.
Source: Journal of Nonlinear Waves
Authors: Seth Minor, Vanja Dukic, David M. Bortz
Institution: University of Colorado Boulder
Language: English
Topic: Nonlinear Waves and Solitons
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Awards: G1322734375, MODULUS: Data-Driven Structured Population Modeling for Prediction of Complex Photosynthetic Phenotypes, Combining Models and Data to Understand the Spatial Dynamics of Host-Pathogen Interactions, CENTER FOR HIERARCHICAL AND ROBUST MODELING OF NON-EQUILIBRIUM TRANSPORT (CHARMNET)
OpenAlex ID: W7167243400