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Literature Cited
C. S. Gardner, J. M. Green, M. D. Kruskal, and R. M. Miura, "Method for solving the KdV equation," Phys. Rev. Lett.,19, No. 19, 1095–1097 (1967).
P. Lax, "Integrals of nonlinear equations of evolution and solitary waves," Commun. Pure. Appl. Math.,21, No. 5, 467–490 (1968).
C. S. Gardner, "Korteweg—de Vries equation and generalizations. IV," J. Math. Phys.,12, No. 8, 1548–1551 (1971).
V. E. Zakharov and L. D. Faddeev, "The Korteweg—de Vries equation is a fully integrable Hamiltonian system," Funkts. Anal. Prilozhen.,5, No. 4, 18–27 (1971).
V. E. Zakharov and A. B. Shabat, "A scheme for the integration of the nonlinear equations of mathematical physics by the method of the inverse scattering problem," Funkts. Anal. Prilozhen.,8, No. 3, 43–53 (1974).
I. M. Krichever, "Reflection-free potentials in a background of finitely zoned ones," Funkts. Anal. Prilozhen.,9, No. 2, 77–78 (1975).
S. P. Novikov, "A periodic problem for the Korteweg—de Vries equation. I,"Funkts'. Anal. Prilozhen.,8, No. 3, 54–66 (1974).
B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, "Nonlinear equations of Korteweg—de Vries type, finitely zoned linear operators, and Abelian manifolds," Usp. Mat. Nauk,30, No. 1, 55–136 (1975).
I. M. Gel'fand and L. A. Dikii, "Asymptotics of the resolvent of the Sturm—Liouville equations and the algebra of the Korteweg—de Vries equations," Usp. Mat. Nauk,30, No. 5, 67–100 (1975).
I. M. Gel'fand and L. A. Dikii, "Lattice of a Lie algebra in formal variational calculus," Funkts. Anal. Prilozhen.,10, No. 1, 18–25 (1976).
L. A. Dikii, "The zeta-function of an ordinary differential equation on a finite segment," Izv. Akad. Nauk SSSR, Ser. Matem.,19, 187–200 (1955).
R. T. Seeley, "The powers As of an elliptic operator," Matematika,12, No. 1, 96–112 (1968).
E. Titchmarsh, Introduction to the Theory of the Fourier Integral, Clarendon Press, Oxford (1937).
I. M. Gel'fand, Yu. I. Manin, and M. A. Shubin, "Poisson brackets and the kernel of a variational derivative in formal variational calculus," Funkts. Anal. Prilozhen.,10, No. 4, 30–34 (1976).
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Moscow State University. Translated from Funktsional'nyi Analiz i Ego Prilozheniya, Vol. 10, No. 4, pp. 13–29, October–December, 1976.
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Gel'fand, I.M., Dikii, L.A. Fractional powers of operators and Hamiltonian systems. Funct Anal Its Appl 10, 259–273 (1976). https://doi.org/10.1007/BF01076025
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DOI: https://doi.org/10.1007/BF01076025