Waves in Continuous Media

  • S. L. Gavrilyuk
  • N.I. Makarenko
  • S.V. Sukhinin

Table of contents

  1. Front Matter
    Pages i-viii
  2. S. L. Gavrilyuk, N. I. Makarenko, S. V. Sukhinin
    Pages 1-41
  3. S. L. Gavrilyuk, N. I. Makarenko, S. V. Sukhinin
    Pages 43-76
  4. S. L. Gavrilyuk, N. I. Makarenko, S. V. Sukhinin
    Pages 77-136
  5. Back Matter
    Pages 137-141

About this book

Introduction

Starting with the basic notions and facts of the mathematical theory of waves illustrated by numerous examples, exercises, and methods of solving typical problems Chapters 1 & 2 show e.g. how to recognize the hyperbolicity property, find characteristics, Riemann invariants and  conservation laws for  quasilinear systems of equations, construct and analyze solutions with weak or strong discontinuities, and how to investigate equations with dispersion and to construct travelling wave solutions for models reducible to nonlinear evolution equations.

Chapter 3 deals with surface and internal waves in an incompressible fluid. The efficiency of mathematical methods is demonstrated on a hierarchy of approximate submodels generated from the Euler equations of homogeneous and non-homogeneous fluids.

The self-contained presentations of the material is complemented by 200+ problems of different level of difficulty, numerous illustrations, and bibliographical recommendations.

Keywords

hyperbolic waves dispersive waves surface internal waves waves

Authors and affiliations

  • S. L. Gavrilyuk
    • 1
  • N.I. Makarenko
    • 2
  • S.V. Sukhinin
    • 3
  1. 1.Aix-Marseille UniversityMarseilleFrance
  2. 2.Russian Academy of Sciences Lavrentyev Institute of HydrodynamicsNovosibirsk State UniversityNovosibirskRussia
  3. 3.Russian Academy of Sciences Lavrentyev Institute of HydrodynamicsNovosibirsk State UniversityNovosibirskRussia

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-49277-3
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-49276-6
  • Online ISBN 978-3-319-49277-3
  • About this book