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The soliton connection. (English) Zbl 0363.35032

MSC:
35P25 Scattering theory for PDEs
35K55 Nonlinear parabolic equations
53B05 Linear and affine connections
76B25 Solitary waves for incompressible inviscid fluids
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[1] GardnerC.S., GreenJ.M., KruskalM.D., and MiuraR.M., Phys. Rev. Letters 19, 1095 (1967). · Zbl 1103.35360 · doi:10.1103/PhysRevLett.19.1095
[2] LaxP.D., Comm. Pure Appl. Math. 21, 467-490 (1968). · Zbl 0162.41103 · doi:10.1002/cpa.3160210503
[3] ZakharovV.E. and ShabatA.B., Zh. Eksp. Teor. Fiz. 61, 118 (1972) = Soviet Phys. JETP 34, 62 (1972).
[4] AblowitzM.J., KaupD.J., NewellA.C., and SegurH., Phys. Rev. Letters 31, 125-127 (1973). · Zbl 1243.35143 · doi:10.1103/PhysRevLett.31.125
[5] AblowitzM.J., KaupD.J., NewellA.C., and SegurH., Studies Appl. Math. 53, 249-315 (1974).
[6] ScottA.C., ChuF.Y.F., and McLaughlinD.W., Proc. I.E.E.E. 61, 1449-1483 (1973), review the whole subject up to that time.
[7] TakhtadzhyanL.A., Zh. Eksp. Teor. Fiz. 66, 476-489 (1974) = Soviet Phys. JETP 39, 228-233 (1974).
[8] ZakharovV.E., TakhtadzhyanL.A., and FaddeevL.D., Dokl. Akad. Nauk USSR 219, 1334-1337 (1974) = Soviet Phys. Dokl. 19, 824-826 (1975).
[9] NewellA.C., Lecture Notes in Mathematics 515, B?cklund Transformations (ed. by R.M.Miura), Springer-Verlag, Berlin etc. 1976, p. 228.
[10] KobayashiS. and NomizuK., Foundations of Differential Geometry, Vol. I, Wiley, New York, 1963.
[11] HermannR. has already, in a different context, pointed out the relevance of SL(2, IR) to the scattering problem: Phys. Rev. Letters 36, 835 (1976). See also Morris, H.C., ?A Prolongation Structure for the AKNS System and its Generalization?, preprint, Trinity College, Dublin 1976. · doi:10.1103/PhysRevLett.36.835
[12] KonnoK. and WadatiM., Prog. Theoret. Phys. 53, 1652-1656 (1975). · Zbl 1079.35505 · doi:10.1143/PTP.53.1652
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