Work

Bi-Hamiltonian structures of KdV type, cyclic Frobenius algebrae and Monge metrics

Year: 2024

Type: article

Abstract: We study algebraic and projective geometric properties of Hamiltonian trios determined by a constant coefficient second-order operator and two first-order localizable operators of Ferapontov–Pavlov type. We show that first-order operators are determined by Monge metrics, and define a structure of cyclic Frobenius algebra. Examples include the AKNS system, a 2-component generalization of Camassa–Holm equation and the Kaup–Broer system. In dimension 2 the trio is completely determined by two conics of rank at least 2. We provide a partial classification in dimension 4.

Source: Journal of Physics A Mathematical and Theoretical

DOI: 10.1088/1751-8121/ad8fe6

Authors: Paolo Lorenzoni, Raffaele Vitolo

Institutions: Istituto Nazionale di Fisica Nucleare, Sezione di Milano Bicocca, University of Milano-Bicocca, University of Salento, Istituto Nazionale di Fisica Nucleare, Sezione di Lecce

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,165