Equivalence of the Darboux and Gardner methods for integrating hyperbolic equations in the plane
David Hartley, Robin W. Tucker, and Philip A. Tuckey
Source: Duke Math. J. Volume 77, Number 1
(1995), 167-192.
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077286150
Mathematical Reviews number (MathSciNet): MR1317631
Zentralblatt MATH identifier: 0823.35121
Digital Object Identifier: doi:10.1215/S0012-7094-95-07707-2
References
[1] A. R. Forsyth, Theory of Differential Equations, Vol. V, VI, Cambridge Univ. Press, Cambridge, 1906.
Zentralblatt MATH: 37.0363.04
[2] R. B. Gardner, The Cauchy problem for Pfaffian systems, Comm. Pure Appl. Math. 22 (1969), 587–596.
Mathematical Reviews (MathSciNet): MR40:6047
Zentralblatt MATH: 0182.42601
Digital Object Identifier: doi:10.1002/cpa.3160220503
[3] R. B. Gardner, A differential geometric generalization of characteristics, Comm. Pure Appl. Math. 22 (1969), 597–626.
Mathematical Reviews (MathSciNet): MR41:618
Zentralblatt MATH: 0182.42602
Digital Object Identifier: doi:10.1002/cpa.3160220504
[4] R. B. Gardner and N. Kamran, Characteristics and the geometry of hyperbolic equations in the plane, J. Differential Equations 104 (1993), no. 1, 60–116.
Mathematical Reviews (MathSciNet): MR94h:58006
Zentralblatt MATH: 0797.35122
Digital Object Identifier: doi:10.1006/jdeq.1993.1064
[5] R. L. Bryant, S. S. Chern, R. B. Gardner, H. L. Goldschmidt, and P. A. Griffiths, Exterior Differential Systems, Math. Sci. Res. Inst. Publ., vol. 18, Springer-Verlag, New York, 1991.
Mathematical Reviews (MathSciNet): MR92h:58007
Zentralblatt MATH: 0726.58002
[6] E. Fackerell, D. Hartley, and R. W. Tucker, An obstruction to the integrability of a class of non-linear wave equations by $1$-stable Cartan characteristics, to appear in J. Differential Equations.
Mathematical Reviews (MathSciNet): MR1308610
Digital Object Identifier: doi:10.1006/jdeq.1995.1009
Duke Mathematical Journal
