Yu. Yu. Bagderina, A. P. Chupakhin, “Invariant and partially invariant solutions of the Green–Naghdi equations”, Prikl. Mekh. Tekh. Fiz., 46:6 (2005), 26–35; J. Appl. Mech. Tech. Phys., 46:6 (2005), 791

Loading [MathJax]/jax/output/SVG/config.js

Prikladnaya Mekhanika i Tekhnicheskaya Fizika

RUS ENG

JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB

JavaScript is disabled in your browser. Please switch it on to enable full functionality of the website

	General information
	Latest issue
	Archive

	Search papers
	Search references

	RSS
	Latest issue
	Current issues
	Archive issues
	What is RSS

Prikl. Mekh. Tekh. Fiz.:
Year:
Volume:
Issue:
Page:
	Find

Personal entry:
Login:
Password:
	Save password
	Enter
	Forgotten password?
	Register

Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2005, Volume 46, Issue 6, Pages 26–35 (Mi pmtf2316)

This article is cited in 8 scientific papers (total in 8 papers)

Invariant and partially invariant solutions of the Green–Naghdi equations

Yu. Yu. Bagderina^a, A. P. Chupakhin^b

^a Institute of Mathematics, Ural Scientific Center, Russian Academy of Sciences, Ufa, 450077, Russia
^b Lavrent'ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090, Russia

Full-text PDF (221 kB) Citations (8)

Abstract: All invariant and partially invariant solutions of the Green–Naghdi equations are obtained that describe the second approximation of shallow water theory. It is proved that all nontrivial invariant solutions belong to one of the following types: Galilean-invariant, stationary, and self-similar solutions. The Galilean-invariant solutions are described by the solutions of the second Painleve equation, the stationary solutions by elliptic functions, and the self-similar solutions by the solutions of the system of ordinary differential equations of the fourth order. It is shown that all partially invariant solutions reduce to invariant solutions.

Keywords: Green–Naghdi equations, invariant and partially invariant solutions, Painleve equation.

Received: 27.01.2005

English version:
Journal of Applied Mechanics and Technical Physics, 2005, Volume 46, Issue 6, Pages 791–799
DOI: https://doi.org/10.1007/s10808-005-0136-z

Bibliographic databases:

Document Type: Article

UDC: 517.9; 532.592

Language: Russian

Citation: Yu. Yu. Bagderina, A. P. Chupakhin, “Invariant and partially invariant solutions of the Green–Naghdi equations”, Prikl. Mekh. Tekh. Fiz., 46:6 (2005), 26–35; J. Appl. Mech. Tech. Phys., 46:6 (2005), 791–799

Citation in format AMSBIB

\Bibitem{BagChu05}

\by Yu.~Yu.~Bagderina, A.~P.~Chupakhin

\paper Invariant and partially invariant solutions of the Green--Naghdi equations

\jour Prikl. Mekh. Tekh. Fiz.

\yr 2005

\vol 46

\issue 6

\pages 26--35

\mathnet{http://mi.mathnet.ru/pmtf2316}

\elib{https://elibrary.ru/item.asp?id=15175980}

\transl

\jour J. Appl. Mech. Tech. Phys.

\yr 2005

\vol 46

\issue 6

\pages 791--799

\crossref{https://doi.org/10.1007/s10808-005-0136-z}

Linking options:

https://www.mathnet.ru/eng/pmtf2316

https://www.mathnet.ru/eng/pmtf/v46/i6/p26

This publication is cited in the following 8 articles:

Alexei Cheviakov, Peng Zhao, CMS/CAIMS Books in Mathematics, 10, Analytical Properties of Nonlinear Partial Differential Equations, 2024, 79
S. V. Meleshko, P. Siriwat, “Group classification of two-dimensional Green–Naghdi equations in the case of time-independent bottom topography”, J. Appl. Mech. Tech. Phys., 63:6 (2022), 972–983
E. I. Kaptsov, S. V. Meleshko, N. F. Samatova, “The one-dimensional Green–Naghdi equations with a time dependent bottom topography and their conservation laws”, Physics of Fluids, 32:12 (2020)
Piyanuch Siriwat, Sergey V. Meleshko, “Group properties of the extended Green–Naghdi equations”, Applied Mathematics Letters, 81 (2018), 1
Piyanuch Siriwat, Chompit Kaewmanee, Sergey V. Meleshko, “Symmetries of the hyperbolic shallow water equations and the Green–Naghdi model in Lagrangian coordinates”, International Journal of Non-Linear Mechanics, 86 (2016), 185
A. Hematulin, P. Siriwat, “Invariant solutions of the special model of fluids with internal inertia”, Communications in Nonlinear Science and Numerical Simulation, 14:5 (2009), 2111
P. Voraka, S. V. Meleshko, “Group classification of one-dimensional equations of fluids with internal energy depending on the density and the gradient of the density”, Continuum Mech. Thermodyn., 20:7 (2009), 397
Apichai Hematulin, Sergey V. Meleshko, Sergey L. Gavrilyuk, “Group classification of one‐dimensional equations of fluids with internal inertia”, Math Methods in App Sciences, 30:16 (2007), 2101

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

Prikladnaya Mekhanika i Tekhnicheskaya Fizika

Statistics & downloads:
Abstract page:	80
Full-text PDF :	22

Registration to the website

Logotypes