Mathematics and Its Applications

Applications of Group-Theoretical Methods in Hydrodynamics

Authors: Andreev, V.K., Kaptsov, O.V., Pukhnachev, V.V., Rodionov, A.A.

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About this book

It was long ago that group analysis of differential equations became a powerful tool for studying nonlinear equations and boundary value problems. This analysis was especially fruitful in application to the basic equations of mechanics and physics because the invariance principles are already involved in their derivation. It is in no way a coincidence that the equations of hydrodynamics served as the first object for applying the new ideas and methods of group analysis which were developed by 1. V. Ovsyannikov and his school. The authors rank themselves as disciples of the school. The present monograph deals mainly with group-theoretic classification of the equations of hydrodynamics in the presence of planar and rotational symmetry and also with construction of exact solutions and their physical interpretation. It is worth noting that the concept of exact solution to a differential equation is not defined rigorously; different authors understand it in different ways. The concept of exact solution expands along with the progress of mathematics (solu­ tions in elementary functions, in quadratures, and in special functions; solutions in the form of convergent series with effectively computable terms; solutions whose searching reduces to integrating ordinary differential equations; etc. ). We consider it justifiable to enrich the set of exact solutions with rank one and rank two in­ variant and partially invariant solutions to the equations of hydrodynamics.

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Group-Theoretic Classification of the Equations of Motion of a Homogeneous or Inhomogeneous Inviscid Fluid in the Presence of Planar and Rotational Symmetry

    Andreev, V. K. (et al.)

    Pages 1-67

  • Exact Solutions to the Nonstationary Euler Equations in the Presence of Planar and Rotational Symmetry

    Andreev, V. K. (et al.)

    Pages 68-127

  • Nonlinear Diffusion Equations and Invariant Manifolds

    Andreev, V. K. (et al.)

    Pages 128-152

  • The Method of Defining Equations

    Andreev, V. K. (et al.)

    Pages 153-180

  • Stationary Vortex Structures in an Ideal Fluid

    Andreev, V. K. (et al.)

    Pages 181-240

Buy this book

eBook 190,39 €
price for Spain (gross)
  • ISBN 978-94-017-0745-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 239,19 €
price for Spain (gross)
  • ISBN 978-0-7923-5215-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 239,19 €
price for Spain (gross)
  • ISBN 978-90-481-5083-0
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Applications of Group-Theoretical Methods in Hydrodynamics
Authors
Series Title
Mathematics and Its Applications
Series Volume
450
Copyright
1998
Publisher
Springer Netherlands
Copyright Holder
Springer Science+Business Media Dordrecht
eBook ISBN
978-94-017-0745-9
DOI
10.1007/978-94-017-0745-9
Hardcover ISBN
978-0-7923-5215-0
Softcover ISBN
978-90-481-5083-0
Edition Number
1
Number of Pages
XII, 396
Topics