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This article is cited in 3 scientific papers (total in 3 papers)
Evolution of Lagrangian Manifolds and Asymptotic Solutions to the Linearized Equations of Gas Dynamics
Anna I. Alliluevaabc, Andrei I. Shafarevichcbad a National Research Centre “Kurchatov Institute”, pl. Akademika Kurchatova 1, Moscow, 123182 Russia
b Moscow Institute of Physics and Technology, Institutskii per. 9, Dolgoprudnyi, 141700 Russia
c Institute for Problems in Mechanics, pr. Vernadskogo 101-1, Moscow, 119526 Russia
d M. V. Lomonosov Moscow State University, Leninskie Gory 1, Moscow, 119991 Russia
Abstract:
We study asymptotic solution of the Cauchy problem for linearized equations of gas dynamics with rapidly oscillating initial data. We construct the formal serie, satisfying this problem. This serie is naturally divided into three parts, corresponding to the hydrodynamic mode and two acoustic modes. The summands of the serie are expressed in terms of the Maslov canonic operator on moving Lagrangian manifolds. Evolution of the manifolds is governed by the corresponding classical Hamiltonian systems.
Keywords:
Lagrangian manifolds, short-wave asymptotics, equations of gas dynamics.
Received: 22.12.2018 Accepted: 09.01.2019
Citation:
Anna I. Allilueva, Andrei I. Shafarevich, “Evolution of Lagrangian Manifolds and Asymptotic Solutions to the Linearized Equations of Gas Dynamics”, Regul. Chaotic Dyn., 24:1 (2019), 80–89
Linking options:
https://www.mathnet.ru/eng/rcd390 https://www.mathnet.ru/eng/rcd/v24/i1/p80
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Abstract page: | 316 | References: | 41 |
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