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Application of Baecklund transformations to the Stokes-Beltrami equations

Published online by Cambridge University Press:  09 April 2009

C. Rogers  and
J. G. Kingston
C. Rogers
Affiliation:
Department of Mathematics The University, Nottingham, England
J. G. Kingston
Affiliation:
Department of Mathematics The University, Nottingham, England
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The Stokes-Beltrami equations, being applicable to many classes of physical problems, have for a long time received a great deal of attention from authors investigating their various aspects. One may cite, for example, Weinstein [1] and more recently Ranger [2] as just two of many research papers into this topic. Baecklund transformations have, in previous work, been applied to hodograph-type equations (Loowrner ], Power, Rogers and Onborn [4], Rogers [5, 6]) and reduction to appropriate canonical forms in elliptic, parabolic, and hyprebolic regimes has been achieved.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 15 , Issue 2 , March 1973 , pp. 179 - 189
Copyright
Copyright © Australian Mathematical Society 1973

References

[1]Weinstein, A., ‘Generalized axially symmetric potential theory’, Bull. Amer. Math. Soc. 59 (1953), 20–28.CrossRefGoogle Scholar
[2]Ranger, K. B., ‘Some integral transformation formulae for the Stokes-Beltrami equations’, J. Math. Mech. 12 (1963), 663–673.Google Scholar
[3]Loewner, C., ‘A transformation theory of partial differential equations of gasdynamics’, NACA, Technical Note 2065 (1950), 1–56.Google Scholar
[4]Power, G., Rogers, C. and Osborn, R. A., ‘Baecklund and generalized Legendre transformations in gasdynamics’, Z. angew. Math. Mech. 49 (1969), 333–340.CrossRefGoogle Scholar
[5]Rogers, C., ‘Transformri Baecklund in magnetogazodinamica Liniarˇ nedisipativ’, Presented to Conferinta National de Mecanic Aplicat, România. (1969).Google Scholar
[6]Rogers, C., ‘Application of Baecklund transformations in aligned magneto-gasdynamics’, Acta Physica Austriaca 31 (1970), 80–88.Google Scholar
[7]Parsons, D. H., ‘Irrotational flow of a liquid with axial symmetry’, Proc. Edin. Math. Soc. 13 (1963) 201–204.CrossRefGoogle Scholar