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Regular and Chaotic Dynamics

, Volume 24, Issue 1, pp 80–89 | Cite as

Evolution of Lagrangian Manifolds and Asymptotic Solutions to the Linearized Equations of Gas Dynamics

  • Anna I. AlliluevaEmail author
  • Andrei I. Shafarevich
Article
  • 4 Downloads

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 

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  • Anna I. Allilueva
    • 1
    • 2
    • 3
    Email author
  • Andrei I. Shafarevich
    • 1
    • 2
    • 3
    • 4
  1. 1.Institute for Problems in MechanicsMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyiRussia
  3. 3.National Research Centre “Kurchatov Institute”MoscowRussia
  4. 4.M. V. Lomonosov Moscow State UniversityMoscowRussia

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