×

On the geometric origin of the equation \(\phi_{11}-\phi_{22} = \exp(\phi)-\exp(-2\phi)\). (English) Zbl 0467.53012


MSC:

53B21 Methods of local Riemannian geometry
53A15 Affine differential geometry
35Q99 Partial differential equations of mathematical physics and other areas of application
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] SasakiR.,Phys. Lett. 71A, 390 (1979);Nucl. Phys. B154, 343 (1979). · doi:10.1016/0375-9601(79)90615-7
[2] LundF. and ReggeT.,Phys. Rev. D14, 1524 (1979). · Zbl 0996.81509 · doi:10.1103/PhysRevD.14.1524
[3] LundF.,Phys. Rev. D15, 1540 (1977). · doi:10.1103/PhysRevD.15.1540
[4] ChineaF. J.,Phys. Lett. 72A, 281 (1979). · doi:10.1016/0375-9601(79)90468-7
[5] BarbashovB. M., NesterenkoV. V., and ChervjakovA. M.,Lett. Math. Phys. 3, 359 (1979);J. Phys. A13, 301 (1980). · doi:10.1007/BF00397208
[6] BarbashovB. M. and NesterenkoV. V.,Fortschritte der Physik 28, 409 (1980). · doi:10.1002/prop.19800280802
[7] EisenhartL. P.,An Introduction to Differential Geometry with Use of the Tensor Calculus, Princeton U.P., Princeton, 1940.
[8] PohlmeyerK.,Commun. Math. Phys. 46, 209 (1976). · Zbl 0996.37504 · doi:10.1007/BF01609119
[9] NeveuA. and PapanicolaouN.,Commun. Math. Phys. 58, 31 (1976). · doi:10.1007/BF01624787
[10] FaddeevL. D. and KorepinV. E.,Phys. Reports 42C, 3 (1978). · doi:10.1016/0370-1573(78)90058-3
[11] BlaschkeW.,Vorlesungen uber Differentialgeometrie, Band, II, Affine Differentialgeometrie, Springer, Berlin, 1923.
[12] FavardJ.,Cours de Geometrie Differentielle Locale, Gauthier-Villars, Paris, 1957.
[13] Veblen, O. and Whitehead, J. H. C.,The Foundations of Differential Geometry, Cambr. Tracts, 1932. · Zbl 0005.21801
[14] MikhailovA. V.,JETP Letters 30, 433 (1979) (in Russian).
[15] ArinsteinA. E., FateyevV. A., and ZamolodchikovA. B.,Phys. Lett. 87B, 389 (1979).
[16] ZhiberA. V. and ShabatA. B.,Dokl. Akad. Nauk S.S.S.R. 247, 1103 (1979) (in Russian).
[17] DoddR. K. and BulloughR. K.,Proc. Roy. Soc. Lon. A352, 481 (1977). · doi:10.1098/rspa.1977.0012
[18] Mikhailov, A. V., Olshanetsky, M. A., and Perelomov, A. M.,Two-dimensional Generalized Toda Lattice, Preprint ITEP-64, Moscow, 1980.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.