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Novikov, S. P.

The periodic problem for the Korteweg-de Vries equation. (English. Russian original) Zbl 0299.35017

Funct. Anal. Appl. 8, 236-246 (1974); translation from Funkts. Anal. Prilozh. 8, No. 3, 54-66 (1974).
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Cited in 16 Reviews
Cited in 118 Documents

MSC:

35G20 Nonlinear higher-order PDEs
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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\textit{S. P. Novikov}, Funct. Anal. Appl. 8, 236--246 (1974; Zbl 0299.35017); translation from Funkts. Anal. Prilozh. 8, No. 3, 54--66 (1974)
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References:

[1] N. I. Akhiezer, ”A continuum analog of orthogonal polynomials in a system of integrals,” Dokl. Akad. Nauk SSSR,141, No. 2, 263-266 (1961).
[2] I. M. Gel’fand and B. M. Levitan, ”On the determination of a differential operator from its spectral function,” Izv. Akad. Nauk SSSR, Ser. Matem.,15, 309-360 (1951). · Zbl 0044.09301
[3] V. A. Marchenko, ”Some questions in the theory of one-dimensional differential operators, I,” Trudy Mosk. Matem. Obshch. I, 327-420 (1952).
[4] L. D. Faddeev, ”Properties of the S-matrix of the one-dimensional Schrödinger equation,” Trudy Matem. Inst. im. V. A. Steklova,73, 314-336 (1964). · Zbl 0145.46702
[5] C. Gardner, J. Green, M. Kruskal, and R. Miura, ”A method for solving the Kortweg?de Vries equation,” Phys. Rev. Lett.,19, 1095-1098 (1967). · Zbl 1103.35360
[6] R. M. Miura, C. S. Gardner, and M. Kruskal, ”Kortweg?de Vries equation and generalizations,” J. Math. Phys.,9, No. 8, 1202-1209 (1968). · Zbl 0283.35018
[7] P. Lax, ”Integrals of nonlinear equations of evolution and solitary waves,” Comm. Pure Appl. Math.,21, No. 2, 467-490 (1968). · Zbl 0162.41103
[8] V. E. Zakharov and L. D. Faddeev, ”The Kortweg?de Vries equation ? a completely integrable Hamiltonian system,” Funkt. Analiz.,5, No. 4, 18-27 (1971).
[9] V. E. Zakharov, ”A kinetic equation for solitons,” Zh. Éksp. Teor. Fiz.,60, No. 3, 993-1000 (1971).
[10] V. E. Zakharov and A. B. Shabat, ”An exact theory of two-dimensional self-focusing and one-dimensional automodulation of waves in nonlinear media,” Zh. Éksp. Teor. Fiz.,61, No. 1, 118-134 (1971).
[11] A. B. Shabat, ”On Kortweg?de Vries equations,” Dokl. Akad. Nauk SSSR,211, No. 6, 1310-1313 (1973).
[12] 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).
[13] R. Hirota, ”Exact solution of the modified Korteweg?de Vries equation for multiple collisions of solitons,” J. Phys. Soc. Japan,33, No. 5, 1456-1458 (1972).
[14] E. L. Ince, ”Further investigations into the periodic Lamé functions,” Proc. Roy. Soc. Edinburgh,60, 83-99 (1940). · Zbl 0027.21201
[15] B. B. Kadomtsev and V. I. Karpman, ”Nonlinear waves,” Usp. Fiz. Nauk,103, No. 2, 193-232 (1971).
[16] V. E. Zakharov and S. B. Manakov, ”On the complete integrability of the nonlinear Schrödinger equation,” Zh. Matem. i Teor. Fiz.,19, No. 3, 322-343 (1974). · Zbl 0293.35025
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