Construction of higher-dimensional nonlinear integrable systems and of their solutions

V. E. Zakharov ; S. V. Manakov

Funkcionalʹnyj analiz i ego priloženiâ, Tome 19 (1985) no. 2, pp. 11-25.

Bibliographie

[1] Zakharov V.E., Shabat A.B., “Skhema integrirovaniya nelineinykh evolyutsionnykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi rasseyaniya. 1”, Funktsion. analiz i ego pril., 8:3 (1974), 43–53 | MR | Zbl

[2] Zakharov V.E., Shabat A.B., “Integrirovanie nelineinykh uravnenii matematicheskoi fiziki metodom obratnoi zadachi rasseyaniya. II”, Funktsion. analiz i ego pril., 13:3 (1979), 13–22 | MR | Zbl

[3] Manakov S.V., “The inverse scattering transform for time-dependent Schrötinger equation and Kadomtsev–Petviashvili equation”, Physics 3D, 3:1–2 (1981), 420–427 | MR

[4] Manakov S.V., Santini P., Takhtajan L.A., “Long-time behavior of the solutions of the Kadomtsev–Petviashvili equation”, Phys. Lett., 74A (1980), 451–454 | DOI | MR

[5] Kaup D.Y. The inverse scattering solution for the full three-dimensional three-wave resonant interaction, Studies Appl. Math., 62 (1980), 75–83 | DOI | MR | Zbl

[6] Ablovitz M.J., Bar Yaacov D., Fokas A.S., “On the inverse scattering transform for the Kadomtsev–Petviashvili equation”, Studies Appl. Math., 69 (1983), 135–143 | DOI | MR

[7] Ablovitz M.J., Fokas A.S., “On the inverse scattering of the time-dependent Schrödinger equation and the associated Kadomtsev–Petviashvili (1) equation”, Studies Appl. Math., 69 (1983), 211–228 | DOI | MR

[8] Zakharov V.E., “The inverses scattering method”, Solitions, ed. Bullough R.K., Caudrey P.J., Springer, 1980, 243–286 ; Solitony, ed. S.P. Novikov, Mir, M., 1983 | DOI | MR | MR

[9] Zakharov V.E., “Integrable systems in multidimensional spaces”, Mathematical problems in theoretical physics, Lect. Notes Phys., 153, 1982, 190–216 | DOI | MR

[10] Zakharov V.E., Mnogomernye integriruemye sistemy, Doklad na Mezhdunarodnom matematicheskom kongresse, Varshava, 1983

[11] Manakov S.V., Nonlocal Rieman problem and solvable multidimentional nonlinear equations, The talk at the NORDITA Landau Institute Workshop. Copenhagen, 1982, September

[12] Zakharov V.E., Manakov S.V., “Mnogomernye nelineinye integriruemye sistemy i metody postroeniya ikh reshenii”, Zap. nauchn. sem. LOMI, 133, 1984, 77–91 | MR | Zbl

[13] Zakharov V.E., Mikhailov A.V., “On the integrability of classical spinor models in two-dimensional space-time”, Comm. Math. Phys., 74 (1980), 4–40 | DOI | MR

[14] Zakharov V.E., Mikhailov A.V., “Variatsionnyi printsip dlya uravnenii, integriruemykh metodom obratnoi zadachi”, Funktsion. analiz i ego pril., 14:1 (1980), 55–56 | MR | Zbl

[15] Manakov S.V., “Metod obratnoi zadachi rasseyaniya i dvumernye evolyutsionnye uravneniya”, UMN, 31:5 (1976), 245 | MR | Zbl

[16] Zhdanov S.K., Trubnikov B.L., “Tsepochki solitonov v plazme s magnitnoi vyazkostyu”, Pisma v ZhETF, 39:3 (1983), 110–113

[17] Zakharov V.E., Manakov S.V., Novikov S.P., Pitaevskii L.P., Teoriya solitonov – metod obratnoi zadachi, Nauka, M., 1980 | MR