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pith:36IAZXMB

pith:2026:36IAZXMBLADN2BE72QKYC32BHN

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A Guide to Applications of $k$-Contact Geometry in Dissipative Field Equations

J. de Lucas, J. Lange, M. Krych

The k-contact Hamilton-De Donder-Weyl formalism supplies explicit Hamiltonian descriptions for many nonlinear dissipative PDEs.

arxiv:2605.13313 v1 · 2026-05-13 · math-ph · math.DG · math.MP

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Claims

C1strongest claim

Our methods yield explicit Hamiltonian descriptions for several nonlinear nonconservative PDEs with polynomial dissipative terms, including damped Klein-Gordon, Allen-Cahn, generalized Burgers, porous medium equations with linear absorption, complex Ginzburg-Landau, damped nonlinear Schrödinger, Fisher-KPP, damped ϕ^4, damped sine-Gordon, and FitzHugh-Nagumo equations, and many others.

C2weakest assumption

That the k-contact Hamilton-De Donder-Weyl formalism on canonical k-contact manifolds and k-contactifications of exact k-symplectic phase spaces can be directly applied to produce well-defined Hamiltonian descriptions for the listed dissipative PDEs without additional ad-hoc adjustments.

C3one line summary

k-contact geometry supplies explicit Hamiltonian descriptions for multiple dissipative PDEs including damped Klein-Gordon, Allen-Cahn, Fisher-KPP, and complex Ginzburg-Landau equations.

References

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[1] Pulsating solitons, chaotic soli- tons, period doubling, and pulse coexistence in mode-locked lasers: Complex Ginzburg- Landau equation approach 2001

[2] Acta Metallurgica27(6), 1085–1095 (1979) https://doi.org/10.1016/0001-6160(79)90196-2 1979 · doi:10.1016/0001-6160(79)90196-2

[3] Conservation laws and variational structure of damped nonlinear wave equations 2024 · doi:10.1002/mma.9798

[4] The World of the Complex Ginzburg–Landau Equa- tion 2002 · doi:10.1103/revmodphys.74

[5] V. I. Arnold.Mathematical Methods of Classical Mechanics. Vol. 60. Graduate Texts in Mathematics. 10.1007/978-1-4757-1693-1. New York: Springer, 1989.isbn: 0387968903 1989 · doi:10.1007/978-1-4757-1693-1

Receipt and verification

First computed	2026-05-18T02:44:48.828819Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

df900cdd815806dd049fd415816f413b5025238d21418f7b934a2d3c4b97207b

Aliases

arxiv: 2605.13313 · arxiv_version: 2605.13313v1 · doi: 10.48550/arxiv.2605.13313 · pith_short_12: 36IAZXMBLADN · pith_short_16: 36IAZXMBLADN2BE7 · pith_short_8: 36IAZXMB

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curl -sH 'Accept: application/ld+json' https://pith.science/pith/36IAZXMBLADN2BE72QKYC32BHN \
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# expect: df900cdd815806dd049fd415816f413b5025238d21418f7b934a2d3c4b97207b

Canonical record JSON

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    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math-ph",
    "submitted_at": "2026-05-13T10:26:21Z",
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