Advertisement

Functional Analysis and Its Applications

, Volume 30, Issue 1, pp 15–22 | Cite as

Invariant integrability criterion for equations of hydrodynamic type

  • M. V. Pavlov
  • R. A. Sharipov
  • S. I. Svinolupov
Article

Keywords

Tensor Field Hydrodynamic Type Riemann Invariant Nijenhuis Tensor Velocity Matrix 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    B. A. Dubrovin and S. P. Novikov, “Hydrodynamics of weakly deformed soliton lattices. Differential geometry and Hamilton's theory,” Usp. Mat. Nauk,44, No. 6, 29–98 (1989).zbMATHMathSciNetGoogle Scholar
  2. 2.
    S. P. Tsarev, “Geometry of Hamiltonian systems of hydrodynamic type. Generalized hodograph method,” Izv. Akad. Nauk SSSR, Ser. Mat.,54, No. 5, 1048–1068 (1990).zbMATHGoogle Scholar
  3. 3.
    A. Haantjes, “OnX n−1-forming sets of eigenvectors,” Indag. Math.,17, No. 2, 158–162 (1955).MathSciNetGoogle Scholar
  4. 4.
    E. V. Ferapontov and S. P. Tsarev, “Systems of hydrodynamic type appearing in chromatography. Riemann invariants and exact solutions,” Mat. Modelirovanie,3, No. 2, 82–91 (1991).MathSciNetGoogle Scholar
  5. 5.
    A. Nijenhuis, “X n−1-forming sets of eigenvectors,” Indag. math.,13, No. 2, 200–212 (1951).zbMATHMathSciNetGoogle Scholar
  6. 6.
    A. Frölicher and A. Nijenhuis, “Some new cohomology invariants for complex manifolds,” Proc. Koninkl. Nederl. Akad. Wetensch. A,59, No. 5, 540–564 (1956).zbMATHGoogle Scholar
  7. 7.
    F. A. Berezin, Introduction into Algebra and Analysis with Anticommuting Variables [in Russian], Moscow State University Press, Moscow (1983).Google Scholar
  8. 8.
    Sh. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 1, Interscience Publishers, New York-London (1963).zbMATHGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • M. V. Pavlov
  • R. A. Sharipov
  • S. I. Svinolupov

There are no affiliations available

Personalised recommendations