Full hamiltonian structure for a parametric coupled Korteweg-de Vries system

TL;DR

This paper derives the complete Hamiltonian framework for a parametric coupled KdV system, revealing its algebraic structure and Poisson geometries, based on a constrained phase space approach.

Contribution

It provides the full Hamiltonian structure for a coupled KdV system, including Poisson pencils and a general observable space, derived via Dirac's constrained system method.

Findings

Hamiltonian structure characterized by Poisson pencils

Derived from four basic Lagrangians

Provides a comprehensive algebraic framework

Abstract

We obtain the full hamiltonian structure for a parametric coupled KdV system. The coupled system arises from four different real basic lagrangians. The associated hamiltonian functionals and the corresponding Poisson structures follow from the geometry of a constrained phase space by using the Dirac approach for constrained systems. The overall algebraic structure for the system is given in terms of two pencils of Poisson structures with associated hamiltonians depending on the parameter of the Poisson pencils. The algebraic construction we present admits the most general space of observables related to the coupled system.