Hamiltonian structure of reductions of the Benney system

TL;DR

This paper demonstrates how to derive Hamiltonian structures for reductions of the Benney chain using conformal maps, providing a systematic approach to understanding their geometric and algebraic properties.

Contribution

It introduces a method to construct Hamiltonian structures for Benney chain reductions from associated conformal maps, linking geometric and integrable systems.

Findings

Hamiltonian structures can be derived from conformal maps.

The approach applies to any reduction of the Benney chain.

Provides a geometric framework for integrable systems.

Abstract

We show how to construct the Hamiltonian structures of any reduction of the Benney chain (dKP) starting from the family of conformal maps associated to it.