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Leznov, A. N.; Smirnov, V. G.

Graded algebras of the second rank and integration of nonlinear equations \(Y_{zz}=\exp(2Y)-\exp(-2Y)\), \(Y_{zz}=2\exp(Y)-\exp(-2Y)\). (English) Zbl 0465.35019

Lett. Math. Phys. 5, 31-36 (1981).
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Cited in 6 Documents

MSC:

35G20 Nonlinear higher-order PDEs
17B70 Graded Lie (super)algebras
35A05 General existence and uniqueness theorems (PDE) (MSC2000)

Keywords:

graded Lie algebras; superalgebras; group representation theory; Lax-type representation; Toda lattice; Cartan matrix; Kac-Moody algebras; periodic problem; sine-Gordon; Dodd-Bullough; Lund-Regge; Volterra equation; difference Korteweg de Vries

Citations:

Zbl 0415.35017; Zbl 0429.35063
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Full Text: DOI

References:

[1] Leznov, A.N., Theor. Math. Phys. 42, v.3 (1980).
[2] LeznovA.N. and SavelievM.V., Lett. Math. Phys. 3, 489 (1979). · Zbl 0415.35017 · doi:10.1007/BF00401930
[3] KacV.G., Izv. Akad. Nauk SSSR, Ser. Mat. 32, 1323 (1968); 34, 385 (1970); Moody, R.V., Bull. Amer. Math. Soc. US. 73, 217 (1967).
[4] JiberA.V. and ShabatA.B., Sov. Phys. Dokl. 247, 1103 (1979).
[5] BogoliubovN.N. and ShirkovD.V., Introduction to the Theory of Quantized Fields, Inter-science Publ., N.Y., 1959.
[6] BogoyavlenskyO.I., Comm. Math. Phys. 51, 261 (1976). · doi:10.1007/BF01617919
[7] FaddeevL.D., Sovrem. Problemy Mat. 3, 93 (1974); Dubrovin, B.A., Matveev, V.B., and Novikov, S.P., Usp. Mat. Nauk. 31, 55 (1976).
[8] LeznovA.N. and SavelievM.V., Phys. Lett. 83, 314 (1979).
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