Literature Cited
M. Ito, Phys. Lett. A,91, 335 (1982).
N. Kh. Ibragimov, Transformation Lie Groups in Mathematical Physics [in Russian], Nauka, Moscow (1983).
B. Fucssteiner and A. S. Fokas, Physica (Utrecht) D,4, 47 (1981).
V. E. Zakharov and L. D. Faddeev, Funktsional. Analiz i Ego Prilozhen.,5, 18 (1971).
V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, The Theory of Solitons (Inverse Scattering Method) [in Russian], Nauka, Moscow (1980).
A. I. Skripnik, A. K. Prikarpatskii, and V. G. Samoilenko, Dokl. Akad. Nauk SSSR, Ser. A, No. 5, 21 (1985).
N. N. Bogolyubov (Jr), A. M. Kurbatov, A. K. Prikarpatskii, and V. G. Samoilenko, Teor. Mat. Fiz.,65, 271 (1985).
P. D. Lax, Commun. Pure Appl. Math.,28, 141 (1975).
Yu. A. Mitropol'skii, A. K. Prikarpatskii, and V. G. Samoilenko, Dokl. Akad. Nauk SSSR,287, 205 (1986).
F. Magri, J. Math. Phys.,19, 1156 (1978).
V. I. Arnol'd, Mathematical Methods of Classical Mechanics (Graduate Texts in Mathematics, Vol. 60), Springer, New York (1978).
V. G. Samoilenko and A. K. Prikarpatskii, Dokl. Akad. Nauk SSSR, Ser. A, No. 3, 22 (1984).
E. V. Doctorov, J. Phys. A,13, 3599 (1980).
Yu. A. Mitropol'skii, A. K. Prikarpatskii, and V. G. Samoilenko, Ukr. Mat. Zh.,36, 451 (1984).
G.-Zh. Tu, Nuovo Cimento B,73, 15 (1983).
N. N. Bogolyubov (Jr), A. K. Prikarpatskii, and V. G. Samoilenko, Dokl. Akad. Nauk SSSR,976, 1225 (1985).
N. N. Bogolyubov (Jr), A. K. Prikarpatskii, and V. G. Samoilenko, Dokl. Akad. Nauk SSSR, Ser. A, No. 10, 51 (1984).
B. A. Dubrovin, S. P. Novikov, and A. T. Fomenko, Modern Geometry [in Russian], Nauka, Moscow (1980).
S.-S. Chern, Complex Manifolds without Potential Theory, Van Nostrand, Princeton (1967).
S. Kobayashi and K. Nomizu, Foundations of Differential Geometry, Vol. 1, Interscience, New York (1963).
B. A. Kupershmidt, Commun. Math. Phys.,99, 51 (1985).
V. B. Natveev and M. I. Yavor, Ann. Inst. Henri Poincaré, Ser. A,31, 25 (1979).
M. Adler, Inv. Math.,50, 219 (1979).
A. K. Prikarpatskii, Teor. Mat. Fiz.,46, 382 (1981).
B. A. Dubrovin, S. P. Novikov, and V. B. Matveev, Usp. Mat. Nauk,31, 55 (1979).
M. Boiti, J. J.-P. Leon, and F. Pempinelli, J. Math. Phys.,25, 1725 (1984).
A. K. Prikarpatskii, Dokl. Akad. Nauk SSSR,253, 298 (1980).
N. N. Bogolyubov (Jr) and A. K. Prikarpatskii, “Application of methods of algebraic geometry,” in: Mathematical Methods and Physicochemical Fields [in Russian], Naukova Dumka, Kiev (1983). Vol. 17, pp. 5–11, Vol. 18, pp. 5–9.
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V. A. Steklov Mathematics Institute, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 67, No. 3, pp. 410–425, June, 1986.
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Bogolyubov, N.N., Prikarpatskii, A.K. Complete integrability of the nonlinear ito and Benney-Kaup systems: Gradient algorithm and lax representation. Theor Math Phys 67, 586–596 (1986). https://doi.org/10.1007/BF01028694
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DOI: https://doi.org/10.1007/BF01028694