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Group theoretical nature of Bäcklund transformations. (English) Zbl 0417.35006

MSC:
35A22 Transform methods (e.g., integral transforms) applied to PDEs
35K55 Nonlinear parabolic equations
35G10 Initial value problems for linear higher-order PDEs
35K25 Higher-order parabolic equations
35Q99 Partial differential equations of mathematical physics and other areas of application
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References:
[1] BäcklundA.V., ?Zur Theorie der Partiellen Differentialgleichungen erster Ordnung?, Mathematische Annalen XVII, 285-328 (1880). · JFM 12.0290.02 · doi:10.1007/BF01446229
[2] ClairinJ., ?Sur les Transformations de Baecklund?, Annales Scientifiques de l’Ecole Normale Supérieure, 3e Série, XIX, supplement, pp. 1-63, (1902).
[3] GoursatE., ?Le Problème de Bäcklund?, Memorial des Sciences Mathématiques, Fasc. VI, Gauthier-Villars, Paris, 1925.
[4] Fokas, A.S., Ph. D. Thesis, California Institute of Technology, 1979.
[5] Ovsjannikov, L.V., ?Group Properties of Differential Equations?, trans. from the Russian by G.W. Bluman, Original publication in 1962.
[6] IbragimovN.H., and AndersonR.L., ?Lie-Bäcklund Tangent Transformations?, JMAA 59, 145-162 (1977).
[7] Anderson, R.L., and Ibragimov, N.H., Lie?Bäcklund transformations in Applications, SIAM Monograph (in press). · Zbl 0447.58001
[8] WahlquistH.D., and EstabrookF.B., ?Bäcklund Transformation for solutions of the Korteweg?de Vries equation. Phys. Rev. Lett. 31, 1386 (1973). · doi:10.1103/PhysRevLett.31.1386
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