The Linearized Korteweg–de Vries Equation on the Line With Metric Graph Defects
Year: 2026
Type: article
Abstract: ABSTRACT We study the small‐amplitude linearization of the Korteweg–de Vries equation on the line with a local defect scattering waves represented by a metric graph domain adjoined at one point. For a representative collection of examples, we derive explicit solution formulas expressed as contour integrals and obtain existence and unicity results for piecewise absolutely continuous data. In so doing, we implement the unified transform method on metric graphs comprising both bonds and leads for a third‐order differential operator.
Source: Studies in Applied Mathematics
DOI: 10.1111/sapm.70208
Author: D. A. Smith
Institution: University of Newcastle Australia
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $4,550
OpenAlex ID: W7148564114