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

2024/03/14 by Giorgio Gubbiotti, Bert van Geemen, Gubbiotti, Giorgio +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2403.09152

openalex publication_date 2024/03/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 how to extend this result for N=6.

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