Least action principle for an integrable shallow water equation

TL;DR

This paper presents a geometric framework for an integrable shallow water equation, demonstrating that fluid configurations evolve through energy-minimizing flows, revealing new insights into the equation's structure.

Contribution

It introduces a geometric approach linking fluid configurations to energy-minimizing flows for an integrable shallow water equation, a novel perspective in the field.

Findings

Fluid configurations are connected via energy-minimizing flows.

The approach reveals a geometric structure underlying the shallow water equation.

Successive fluid states are uniquely determined by a least action principle.

Abstract

For an integrable shallow water equation we describe a geometrical approach showing that any two nearby fluid configurations are successive states of a unique flow minimizing the kinetic energy.