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Nonlinear Sciences > Exactly Solvable and Integrable Systems

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

Authors: Pierandrea Vergallo, Evgeny V. Ferapontov
(Submitted on 2 Dec 2022 (v1), last revised 2 Sep 2023 (this version, v3))
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).
Subjects: Exactly Solvable and Integrable Systems (nlin.SI); Mathematical Physics (math-ph); Pattern Formation and Solitons (nlin.PS)
MSC classes: 35K55, 35Q58, 37K10
Cite as: arXiv:2212.01413 [nlin.SI]
  (or arXiv:2212.01413v3 [nlin.SI] for this version)

Submission history

From: Pierandrea Vergallo [view email]
[v1] Fri, 2 Dec 2022 19:23:31 GMT (12kb)
[v2] Fri, 26 May 2023 22:39:21 GMT (14kb)
[v3] Sat, 2 Sep 2023 08:13:31 GMT (15kb)
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