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
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 VriesReferences:
[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). |
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.