Hamiltonian systems of Jordan block type: delta-functional reductions of the kinetic equation for soliton gas

Evgeny V. Ferapontov; Pierandrea Vergallo

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Hamiltonian systems of Jordan block type: delta-functional reductions of the kinetic equation for soliton gas

Pierandrea Vergallo, Evgeny V. Ferapontov

Exactly Solvable and Integrable Systems · Submitted 2 Dec 2022

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures.

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arXiv ID2212.01413 (version 3)

Pith ID3G74WA6J, Pith's permanent record of this paper and its review

CitationEvgeny V. Ferapontov, Pierandrea Vergallo. "Hamiltonian systems of Jordan block type: delta-functional reductions of the kinetic equation for soliton gas." arXiv:2212.01413 (2022). https://pith.science/paper/3G74WA6J

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We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures. Multi-Hamiltonian formulation of linearly degenerate systems governing delta-functional reductions of the kinetic equation for dense soliton gas is established (for KdV, sinh-Gordon, hard-rod, Lieb-Liniger, DNLS, and separable cases).

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures.	result 0.95	0.86	0.46	asserted 1.00
s1	Multi-Hamiltonian formulation of linearly degenerate systems governing delta-functional reductions of the kinetic equation for dense soliton gas is established (for KdV, sinh-Gordon, hard-rod, Lieb-Liniger, DNLS, and separable cases).	contribution 0.74	0.92	0.52	asserted 1.00

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Original abstract

We demonstrate that linear degeneracy is a necessary condition for quasilinear systems of Jordan block type to possess first-order Hamiltonian structures. Multi-Hamiltonian formulation of linearly degenerate systems governing delta-functional reductions of the kinetic equation for dense soliton gas is established (for KdV, sinh-Gordon, hard-rod, Lieb-Liniger, DNLS, and separable cases).

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2 arXiv papers cite this in 2 sentences

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Cites as background 2 papers

Systems of this kind naturally arise in applications as degenerations of hydrodynamic systems associated with multi-dimensional hypergeometric functions [ref] , in the context of parabolic regularisation of the Riemann equation [ref] , as reductions of hydrodynamic chains and linearly degenerate dispersionless PDEs in 3D [ref] , in the context of Nijenhuis geometry [ref] , and as primary flows of non-semisimple Frobenius manifolds [ref] .

Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures · Introduction · 0.95
We refer to [ref] for further discussion and references.

Hydrodynamic scales of integrable many-particle systems · Kinetic equation for soliton gas: reductions of Jordan block type · 1.00

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