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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 215, Number 2, Pages 165–175
DOI: https://doi.org/10.4213/tmf10393 (Mi tmf10393) 		 
Cauchy invariants and exact solutions of nonlinear equations of hydrodynamics

A. A. Abrashkinab, E. N. Pelinovskyab

a National Research University "Higher School of Economics", Nizhny Novgorod, Russia
b Federal Research Center, Institute of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, Russia
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DOI: https://doi.org/10.4213/tmf10393
Abstract: We review exact solutions for gravity waves in deep water. All of them are obtained within the Lagrangian framework and are generalizations of Gerstner waves (to the cases of inhomogeneous pressure on the free surface and taking the rotation of the fluid into account). The Cauchy invariants are found for each type of waves.
Keywords: Lagrangian coordinates, Cauchy invariants, Gerstner wave.
Funding agency Grant number
Russian Science Foundation 19-12-00253
E. N. Pelinovsky appreciates the support from the Russian Science Foundation under grant No. 19-12-00253.
Received: 01.11.2022
Revised: 28.11.2022
English version:
Theoretical and Mathematical Physics, 2023, Volume 215, Issue 2, Pages 599–608
DOI: https://doi.org/10.1134/S004057792305001X
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: A. A. Abrashkin, E. N. Pelinovsky, “Cauchy invariants and exact solutions of nonlinear equations of hydrodynamics”, TMF, 215:2 (2023), 165–175; Theoret. and Math. Phys., 215:2 (2023), 599–608
Citation in format AMSBIB
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\pages 165--175
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\jour Theoret. and Math. Phys.
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\pages 599--608
\crossref{https://doi.org/10.1134/S004057792305001X}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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