Skip to main content
SpringerLink
Log in

Symmetries and Conservation Laws of the Equations of Two-Dimensional Shallow Water Over Uneven Bottom

  • Chapter
  • First Online:
Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics

Part of the book series: Understanding Complex Systems ((UCS))

  • 541 Accesses

Abstract

A system of equations of two-dimensional shallow water over uneven bottom is considered. Overdetermined systems of equations for determining the symmetries and the conservation laws are obtained. The compatibilities of this overdetermined systems of equations are investigated. The general forms of the solutions of the overdetermined systems are found. The kernels of the symmetry operators and conservation laws are found. Cases of kernels extensions of symmetry operators and conservation laws are presented. The corresponding classifying equations are given. The results of the group classification have indicated that the system of equations of two-dimensional shallow water over uneven bottom cannot be linearized by point transformation in contrast to the system of equations of one-dimensional shallow water in the cases of horizontal and inclined bottom profiles.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 119.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 159.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Aksenov, A.V., Druzhkov, K.P.: Conservation laws and symmetries of the shallow water system above rough bottom. J. Phys.: Conf. Ser. 722(012001), 1–7 (2016)

    Google Scholar 

  2. Stoker, J.J.: Water Waves. The Mathematical Theory With Applications. Interscience Publishers, New York (1957)

    MATH  Google Scholar 

  3. Aksenov, A.V., Druzhkov, K.P.: Symmetries of the equations of two-dimensional shallow water over a rough bottom. J. Phys.: Conf. Ser. 1205(012002), 1–7 (2019)

    Google Scholar 

  4. Ovsiannikov, L.V.: Group Analysis of Differential Equations. Academic, New York (1982)

    MATH  Google Scholar 

Download references

Acknowledgements

The research was supported by the Russian Science Foundation (grant no. 18-11-00238).

Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, GSP-1 Leninskie Gory, 119991, Moscow, Russian Federation

    A. V. Aksenov & K. P. Druzhkov

Authors
  1. A. V. Aksenov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. K. P. Druzhkov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Aksenov .

Editor information

Editors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

  2. National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    Michael Z. Zgurovsky

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Aksenov, A.V., Druzhkov, K.P. (2021). Symmetries and Conservation Laws of the Equations of Two-Dimensional Shallow Water Over Uneven Bottom. In: Sadovnichiy, V.A., Zgurovsky, M.Z. (eds) Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-50302-4_7

Download citation

Publish with us

Policies and ethics

Search

Navigation