Solitons, Euler’s equation, and vortex patch dynamics

Publisher Website
Google Scholar
Abstract
Integrable systems related to the Korteweg–de Vries (KdV) equation are shown to be associated with the dynamics of vortex patches in ideal two-dimensional fluids. This connection is based on a truncation of the exact contour dynamics analogous to the ‘‘localized induction approximation’’ which relates the nonlinear Schrödinger equation to the motion of a vortex filament. Single soliton solutions of the periodic modified KdV problem correspond to uniformly rotating shapes which approximate the Kirchoff ellipse and known generalizations. A simple geometrical interpretation of the dual Poisson bracket structure of the modified KdV hierarchies is given.

This publication has 25 references indexed in Scilit: