Advertisement

Il Nuovo Cimento B (1971-1996)

, Volume 83, Issue 2, pp 127–134 | Cite as

The Burgers hierarchy: on nonlinear initial and boundary value problems

  • C. Rogers
  • P. L. Sachdev
Article

Summary

Systems of nonlinear equations of the Burgers-hierarchy type are reduced to linear canonical form via Bäcklund transformations with a view to the treatment of initial and nonlinear boundary value problems.

PACS. 02.30

Function theory analysis 

Иерархия Бургеса. О проблемах начальных и нелинейных граничных условий

Резюме

Системы нелинейных уравнений типа иерархии Бургерса сводятся к линейной канонической форме с помощью преобразований Бэклунда с целью исследования проблем начальных и нелинейных граничных условий.

Riassunto

Sistemi di equazioni non lineari del tipo della gerarchia di Burgers sono ridotti a una forma canonica lineare attraverso trasformazioni di Bäcklund tenendo conto del trattamento dei problemi del valore limite iniziale e non lineare.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. (1).
    E. Hopf:Commun. Pure Appl. Math.,3, 201 (1950).MathSciNetCrossRefGoogle Scholar
  2. (2).
    J. D. Cole:Q. Appl. Math.,9, 225 (1951).zbMATHGoogle Scholar
  3. (3).
    P. L. Sachdev:Z. Angew. Math. Phys.,29, 963 (1978).MathSciNetCrossRefzbMATHGoogle Scholar
  4. (4).
    H. Tasso andJ. Teichmann:Z. Angew. Math. Phys. 30, 1023 (1979).MathSciNetCrossRefzbMATHGoogle Scholar
  5. (5).
    D. Levi, O. Ragnisco andM. Bruschi:Nuovo Cimento B,74, 33 (1983).MathSciNetADSCrossRefGoogle Scholar
  6. (6).
    S. de Filippo, M. Salerno andG. Vilasi: Preprint Instituto di Fisica dell’Università, Salerno, Italia.Google Scholar
  7. (7).
    B. E. Ciothier, J. H. Knight andI. White:Soil Sci.,132, 255 (1981).CrossRefGoogle Scholar
  8. (8).
    C. Rogers, M. P. Stallybrass andD. L. Clements:Nonlinear Analysis Theory, Methods and Applications,7, 785 (1983).MathSciNetCrossRefzbMATHGoogle Scholar
  9. (9).
    C. Rogers, H. Rasmussen andM. P. Stallybrass:Int. J. Multi-Phase Flow,10, 95 (1984).CrossRefzbMATHGoogle Scholar
  10. (10).
    A. S. Fokas andY. C. Yortsos:SIAM J. Appl. Math.,42, 318 (1982).MathSciNetCrossRefGoogle Scholar
  11. (11).
    C. Rogers andW. F. Shadwick:Bäcklund Transformations and Their Applications (Academic Press, New York, N.Y., 1982).zbMATHGoogle Scholar
  12. (12).
    J. G. Kingston andC. Rogers:Phys. Lett. A,92, 216 (1982).MathSciNetCrossRefGoogle Scholar
  13. (13).
    J. G. Kingston andC. Rogers:Q. Appl. Math.,51, 423 (1984).Google Scholar
  14. (14).
    H. C. Thomas:J. Am. Chem. Soc.,66, 1664, (1944).CrossRefzbMATHGoogle Scholar
  15. (15).
    G. B. Whitham:Linear and Nonlinear Waves (John Wiley, New York, N.Y., 1974).zbMATHGoogle Scholar
  16. (16).
    S. Goldstein:Proc. R. Soc. London, Ser. A,219, 151 (1953).ADSCrossRefzbMATHGoogle Scholar
  17. (17).
    S. Goldstein andJ. D. Murray:Proc. R. Soc. London, Ser. A,252, 334 (1959).MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Società Italiana di Fisica 1984

Authors and Affiliations

  • C. Rogers
    • 1
  • P. L. Sachdev
    • 2
  1. 1.Department of Applied MathematicsUniversity of WaterlooWaterlooCanada
  2. 2.Courant InstituteNew YorkUSA

Personalised recommendations