Korteweg-de Vries equation: a completely integrable Hamiltonian system. (English. Russian original) Zbl 0257.35074

Funct. Anal. Appl. 5, 280-287 (1972); translation from Funkts. Anal. Prilozh. 5, No. 4, 18-27 (1971).


35Q53 KdV equations (Korteweg-de Vries equations)
35J10 Schrödinger operator, Schrödinger equation
35P25 Scattering theory for PDEs
Full Text: DOI


[1] C. S. Gardner, J. M. Greene, M. D. Kruskal, and R. M. Miura, ”Method for solving the Korteweg-de Vries equation,” Phys. Rev. Lett.,19, 1095-1097 (1967). · Zbl 1103.35360
[2] R. M. Miura, C. S. Gardner, and M. D. Kruskal, ”Korteweg-de Vries equation and generalizations, II. Existence of conservation laws and constants of motion,” J. Math. Phys.,9, No. 8, 1204-1209 (1968). · Zbl 0283.35019
[3] M. D. Kruskal, R. M. Miura, C. S. Gardner, and N. J. Zabusky, ”Korteweg-de Vries equation and generalizations, V. Uniqueness and nonexistence of polynomial conservation laws,” J. Math. Phys.,11, No. 3, 952-960 (1970). · Zbl 0283.35022
[4] P. D. Lax, ”Integrals of nonlinear equations and solitary waves” Comm. Pure Appl. Math.,21, No. 2, 467-490 (1968). · Zbl 0162.41103
[5] L. D. Faddeev, ”Properties of the S-matrix of the one-dimensional Schroedinger equation,” Trudy Matem. in-ta im. V. A. Steklova,73, 314-336 (1964). · Zbl 0145.46702
[6] J. Kay and H. E. Moses, ”The determination of the scattering potential from the spectral measure function, III” Nuovo Cimento,3, No. 2, 277-304 (1956).
[7] L. D. Landau and E. M. Lifshits, Mechanics, Addison-Wesley, Reading, Mass (1960).
[8] V. I. Arnol’d, Lectures on Classical Mechanics [in Russian], Moscow State Univ., Moscow (1968).
[9] I. M. Gel’fand and B. M. Levitan, ”On a simple identity for the characteristic values of a differential operator of the second order,” Dokl. Akad. Nauk SSSR,88, No. 4, 593-596 (1953).
[10] I. M. Gel’fand, ”On identities for characteristic values of a differentiable operator of the second order,” Usp. Mat. Nauk,11, No. 1, 191-198 (1956).
[11] V. S. Buslaev and L. D. Faddeev, ”On formulas for traces of a Sturm-Liouville singular differential operator,” Dokl. Akad. Nauk SSSR, 132, No. 1, 13-16 (1960). · Zbl 0129.06501
[12] V. E. Zakharov, ”A kinetic equation for solitons,” Zh. Éksp. Teor. Fiz.,60, No. 3, 993-1000 (1971).
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