A new mechanism for the emergence of KdV

 The paper “A universal form for the emergence of the Korteweg-de Vries equation” by Tom Bridges has appeared in the Proc Roy Soc London A. The paper presents a new theory, based on modulation, for the emergence of KdV.  Only a single necessary condition needs to be satisfied (criticality) and the coefficient of the nonlinear term in the emergent KdV equation is determined by the curvature of a momentum map.  One implication is that the assumption of shallow water is neither necessary nor sufficient for the emergence of KdV as a model for water waves.  An electronic version of the paper can be downloaded here.