On the hamiltonian formulation of an octonionic integrable extension for the Korteweg-de Vries equation

TL;DR

This paper develops a Hamiltonian framework for an octonionic extension of the Korteweg-de Vries equation, addressing its non-commutative and non-associative algebraic properties and analyzing its Poisson structure.

Contribution

It introduces a Hamiltonian formulation for the octonionic KdV extension, incorporating its unique algebraic features and proposing a parametric master Lagrangian with dual Hamiltonian structures.

Findings

Hamiltonian formulation for octonionic KdV derived

Poisson structure analyzed in the octonionic context

A parametric master Lagrangian encompassing two Hamiltonian structures

Abstract

We present in this work the hamiltonian formulation of an octonionic extension for the Korteweg-de Vries equation. The formulation takes into account the non commmutativity and non associativity of the implicit algebra which defines the equation. We also analize the Poisson structure of the hamiltonian formulation. We propose a parametric master Lagrangian which contains the two hamiltonian structures of the integrable octonionic equation.