Work

Line geometry of pairs of second-order Hamiltonian operators and quasilinear systems

Year: 2024

Type: article

Abstract: We demonstrate that a pair consisting of a second-order homogeneous Hamiltonian structure in N components and its associated system of conservation laws is in bijective correspondence with an alternating three-form on a N + 2 -dimensional vector space. Additionally, we show that the three-form offers N + 2 linear equations in the Plücker coordinates that define the associated line congruence. We utilize these results to characterize systems of conservation laws with second-order structure for N ≤ 4 . We finally comment on how to extend this result for N = 6 .

Source: Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences

DOI: 10.1098/rspa.2024.0280

Authors: G. Gubbiotti, B. van Geemen, P. Vergallo

Institutions: University of Milan, Istituto Nazionale di Fisica Nucleare, Sezione di Milano, University of Messina

Language: English

Topic: Nonlinear Waves and Solitons

Subfield: Statistical and Nonlinear Physics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Istituto Nazionale di Alta Matematica "Francesco Severi", European Commission, Istituto Nazionale di Fisica Nucleare, Gruppo Nazionale per la Fisica Matematica

Award: G3793356882