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Literature Cited
C. S. Gardner, J. M. Green, M. Kruskal, and R. M. Miura, "Method for solving the Korteweg—de Vries equation," Phys. Rev. Lett.,19, 1095–1097 (1967).
P. D. Lax, "Integrals of nonlinear equations of evolution and solitary waves," Comm. Pure Appl. Math.,21, 467–490 (1968).
V. E. Zakharov and A. B. Shabat, "A refined theory of two-dimensional self-focussing and one-dimensional self-modulation of waves in nonlinear media," Zh. Éksp. Teor. Fiz.,61, No. 1, 118–134 (1971).
V. E. Zakharov and A. B. Shabat, "On the interaction of solitons in a stable medium," Zh. Éksp. Teor. Fiz.,64, No. 5, 1627–1639 (1973).
V. E. Zakharov, "The method of the inverse scattering problem," in: Theory of Elastic Media with Microstructure, edited by I. A. Kukin [in Russian], Nauka, Moscow (1974).
A. B. Shabat, "Concerning the Korteweg—de Vries equation," Dokl. Akad. Nauk SSSR,211, No. 6, 1310–1313 (1973).
V. E. Zakharov, "On the problem of one-dimensional stochastized circuits of nonlinear oscillators," Zh. Éksp. Teor. Fiz.,65, No. 1, 219–225 (1973).
B. B. Kadomtsev and V. I. Petviashvili, "On the stability of solitary waves in weakly dispersive media," Dokl. Akad. Nauk SSSR,192, No. 4, 753–756 (1970).
M. Wadati and M. Toda, "Exact N-soliton solution of the Korteweg—de Vries equation," J. Phys. Soc. Japan,36, 1403–1412 (1972).
V. E. Zakharov and S. V. Manakov, "On resonance interaction of wave packets in nonlinear media," ZhÉTF Pis. Red.,18, No. 7, 413 (1973).
N. Bloembergen, Nonlinear Optics, W. A. Benjamin (1965).
V. E. Zakharov, L. A. Takhtadzhyan, and L. D. Faddeev, "Complete description of the solutions of the ‘sin—gordon’ equation," Dokl. Akad. Nauk SSSR (1974).
S. V. Manakov, "On a theory of the two-dimensional stationary self-focussing electromagnetic waves," Zh. Éksp. Teor. Fiz.,65, 505–516 (1973).
M. Wadati, "The modified Korteweg—de Vries equation," J. Phys. Soc. Japan,34, No. 5, 1289–1291 (1973).
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L. D. Landau Institute of Theoretical Physics. Bashkir State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 8, No. 3, pp. 43–53, July–September, 1974.
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Zakharov, V.E., Shabat, A.B. A scheme for integrating the nonlinear equations of mathematical physics by the method of the inverse scattering problem. I. Funct Anal Its Appl 8, 226–235 (1974). https://doi.org/10.1007/BF01075696
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DOI: https://doi.org/10.1007/BF01075696