M. V. Pavlov, “Hamiltonian formalism of weakly nonlinear hydrodynamic systems”, TMF, 73:2 (1987), 316–320; Theoret. and Math. Phys., 73:2 (1987), 1242

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Teoreticheskaya i Matematicheskaya Fizika, 1987, Volume 73, Number 2, Pages 316–320 (Mi tmf5634)

This article is cited in 22 scientific papers (total in 22 papers)

Hamiltonian formalism of weakly nonlinear hydrodynamic systems

M. V. Pavlov

Full-text PDF (434 kB) Citations (22)

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Abstract: Systems of quasilinear equations are considered which are diagonalizable and Hamiltonian, with the condition

$\partial_iv^i=0$ where

$u_t^i=v^i(u)u_x^i$ ,

$i=1,\dots,N$ . Conservation laws of such systems are found as well as metrics and Poisson brackets. By concrete examples the procedure of finding the solutions is demonstrated. Conditions of the existence of solutions and continuity of commuting flows are pointed out.

Received: 15.12.1986

English version:
Theoretical and Mathematical Physics, 1987, Volume 73, Issue 2, Pages 1242–1245
DOI: https://doi.org/10.1007/BF01017597

Bibliographic databases:

Language: Russian

Citation: M. V. Pavlov, “Hamiltonian formalism of weakly nonlinear hydrodynamic systems”, TMF, 73:2 (1987), 316–320; Theoret. and Math. Phys., 73:2 (1987), 1242–1245

Citation in format AMSBIB

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\jour Theoret. and Math. Phys.

\yr 1987

\vol 73

\issue 2

\pages 1242--1245

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Linking options:

https://www.mathnet.ru/eng/tmf5634

https://www.mathnet.ru/eng/tmf/v73/i2/p316

This publication is cited in the following 22 articles:

T. Congy, H.T. Carr, G. Roberti, G.A. El, “Riemann problem for polychromatic soliton gases: A testbed for the spectral kinetic theory”, Wave Motion, 2025, 103480
Thibault Bonnemain, Vincent Caudrelier, Benjamin Doyon, “Hamiltonian Formulation and Aspects of Integrability of Generalised Hydrodynamics”, Ann. Henri Poincaré, 2025
S. V. Agapov, Zh. Sh. Fakhriddinov, “O nekotorykh svoistvakh polugamiltonovykh sistem, voznikayuschikh v zadache ob integriruemykh geodezicheskikh potokakh na dvumernom tore”, Sib. matem. zhurn., 64:5 (2023), 881–894
S. V. Agapov, Zh. Sh. Fakhriddinov, “On Some Properties of Semi-Hamiltonian Systems Arising in the Problem of Integrable Geodesic Flows on the Two-Dimensional Torus”, Sib Math J, 64:5 (2023), 1063
Makridin V Z. Pavlov V M., “Multidimensional Conservation Laws and Integrable Systems II”, Stud. Appl. Math., 148:2 (2022), 813–824
A. M. Kamchatnov, D. V. Shaykin, “Dynamics of Interaction between Two Soliton Clouds”, J. Exp. Theor. Phys., 135:5 (2022), 768
El G.A., “Soliton Gas in Integrable Dispersive Hydrodynamics”, J. Stat. Mech.-Theory Exp., 2021:11 (2021), 114001
Yarema A. Prykarpatskyy, “Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin's Integrability Classification of Perturbed KdV-Type Equations”, Symmetry, 13:6 (2021), 1077
R. Ch. Kulaev, A. B. Shabat, “Darboux system and separation of variables in the Goursat problem for a third order equation in $\mathbb {R}^3$ ”, Russian Math. (Iz. VUZ), 64:4 (2020), 35–43
Marvan M. Pavlov M.V., “Integrable Dispersive Chains and Their Multi-Phase Solutions”, Lett. Math. Phys., 109:5 (2019), 1219–1245
Maxim V. Pavlov, “Integrability of exceptional hydrodynamic-type systems”, Proc. Steklov Inst. Math., 302 (2018), 325–335
Pavlov M.V., “Integrable Dispersive Chains and Energy Dependent Schrodinger Operator”, J. Phys. A-Math. Theor., 47:29 (2014), 295204
M. V. Pavlov, V. B. Taranov, G. A. El, “Generalized hydrodynamic reductions of the kinetic equation for a soliton gas”, Theoret. and Math. Phys., 171:2 (2012), 675–682
El G.A., Kamchatnov A.M., Pavlov M.V., Zykov S.A., “Kinetic Equation for a Soliton Gas and Its Hydrodynamic Reductions”, J Nonlinear Sci, 21:2 (2011), 151–191
Lorenzoni P., Pedroni M., “Natural Connections for Semi-Hamiltonian Systems: The Case of the epsilon-System”, Lett Math Phys, 97:1 (2011), 85–108
Blaszak, M, “A COORDINATE-FREE CONSTRUCTION OF CONSERVATION LAWS AND RECIPROCAL TRANSFORMATIONS FOR A CLASS OF INTEGRABLE HYDRODYNAMIC-TYPE SYSTEMS”, Reports on Mathematical Physics, 64:1–2 (2009), 341
PARTHA GUHA, “TRANSVECTANT, INTEGRABILITY AND THE BORN–INFELD EQUATION”, Mod. Phys. Lett. A, 19:10 (2004), 775
Ferapontov, EV, “Reciprocal transformations of Hamiltonian operators of hydrodynamic type: Nonlocal Hamiltonian formalism for linearly degenerate systems”, Journal of Mathematical Physics, 44:3 (2003), 1150
E. V. Ferapontov, “Integration of weekly nonlinear semi-hamiltonian systems of hydrodynamic type by methods of the theory of webs”, Math. USSR-Sb., 71:1 (1992), 65–79
V. R. Kudashev, S. E. Sharapov, “Generalized hodograph method from the group-theoretical point of view”, Theoret. and Math. Phys., 85:2 (1990), 1155–1159

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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