Geodesic
A (3+1)-dimensional equation admitting a Lax representation
Izvestiya. Mathematics, Tome 40 (1993) no. 1, pp. 225-233 Cet article a éte moissonné depuis la source Math-Net.Ru

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An equation is found that is the second in the hierarchy of higher order equations connected with Dym's equation; equations on the scattering data are introduced; its $(3+1)$-dimensional analogue is considered which admits a Lax representation with the same operator $L$ and an operator $A$ including differentiation with respect to the additional variables; the presence of a countable family of integrable discretizations of the second Korteweg–de Vries equation is demonstrated. 
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     title = {A (3+1)-dimensional equation admitting a {Lax} representation},
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A. S. Piskunov. A (3+1)-dimensional equation admitting a Lax representation. Izvestiya. Mathematics, Tome 40 (1993) no. 1, pp. 225-233. http://geodesic.mathdoc.fr/item/IM2_1993_40_1_a6/

[1] Kruskal M., “Non-linear wave equations”, Lecture Notes in Physics, 38, Springer-Verlag, Berlin, Heidelberg, New York, 1975, 310–354 | MR

[2] Zakharov V. E., Manakov S. V., Novikov S. P., Pitaevskii L. P., Teoriya solitonov, Nauka, M., 1980 | MR

[3] Takhtadzhyan L. A., Faddeev L. D., Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR | Zbl

[4] Bogoyavlenskii O. I., “Oprokidyvayuschiesya solitony v dvumernykh integriruemykh uravneniyakh”, UMN, 45:4 (1990), 17–77 | MR | Zbl

[5] Bogoyavlenskii O. I., “Oprokidyvayuschiesya solitony, IV”, Izv. AN SSSR. Ser. matem., 54:6 (1990), 1123–1133 | MR | Zbl

[6] Sabatier P. C., “Around the classical string problem”, Lecture Notes in Physics, 120, Springer-Verlag, Berlin, Heidelberg, New York, 1980, 85–102 | MR

[7] Bogoyavlenskii O. I., “Algebraicheskie konstruktsii nekotorykh integriruemykh uravnenii”, Izv. AN SSSR. Ser. matem., 52:4 (1988), 712–739 | MR

[8] Bogoyavlenskii O. I., “Nekotorye konstruktsii integriruemykh dinamicheskikh sistem”, Izv. AN SSSR. Ser. matem., 51:4 (1987), 737–767 | MR

[9] Zakharov V. E., Faddeev L. D., “Uravnenie KdF – vpolne integriruemaya gamiltonova sistema”, Funktsion. analiz i ego prilozh., 5:4 (1971), 18–27 | MR | Zbl

[10] Moser J., “Three Integrable Hamiltonian Systems Connected with Isospectral Deformations”, Adv. in Math., 16 (1975), 197–220 | DOI | MR | Zbl