References
Benjamin, T.B., The stability of solitary waves. Proc. Roy. Soc. London 328A, 153–183 (1972).
Borg, G., Eine Umkehrung der Sturm-Liouvillschen Eigenwertaufgabe. Bestimmung der Differentialgleichung durch die Eigenwerte. Acta Math. 78, 1–96 (1946).
Buslaev, V.S., & L.D. Faddeev, On trace formulas for singular Sturm-Liouville operators (in Russian). Dokl. Akad. Nauk. SSSR 132, 13–16 (1960).
van der Corput, J.G., Asymptotic developments I. Fundamental theorems of asymptotics. J. Anal. Math. 4, 341–418 (1955).
Dikii, L.A., Zeta-functions for ordinary differential operators on a finite interval (in Russian). Izv. Akad. Nauk SSSR, Ser. Mat. 19, 187–200 (1955).
Dikii, L.A., Trace formulas for Sturm-Liouville differential operators. AMS Translations 18, 81–115 (1958).
Flaschka, H., On the Toda lattice II. Inverse scattering solution. Prog. Theor. Phys. 51, 703–716 (1974).
Gardner, C.S., Korteweg-deVries equation and generalizations IV. The Korteweg-deVries equation as a Hamiltonian system. J. Math. Phys. 13, 1548–1551 (1971).
Gardner, C.S., J.M. Greene, M.D. Kruskal, & R.M. Miura, Method for solving the Kortewegde-Vries equations. Phys. Rev. Lettr. 19, 1095–1097 (1967).
Gardner, C.S., J.M. Greene, M.D. Kruskal, & R.M. Miura, Korteweg-deVries equation and generalizations VI. Methods for exact solution. Comm. Pure. Appl. Math. 27, 97–133 (1974).
Gel'fand, L.M., B.M. Levitan, On a simple identity for the eigenvalues of a second-order differential operator (in Russian). Dokl. Akad. Nauk SSSR 88, 953–956 (1953).
Gel'fand, I.M., On identities for the eigenvalues of a second-order differential operator (in Russian). Uspehi Mat. Nauk 11, 191–198 (1956).
Hochstadt, H., On the determination of a Hill's equation from its spectrum. Arch. Rational Mech. Anal. 19, 353–362 (1965).
Jacobson, N., Lectures in Abstract Algebra, v. I. Princeton: D. Van Nostrand 1951.
Lax, P.D., Integrals of nonlinear equations of evolution and solitary waves. Comm. Pure Appl. Math. 21, 467–490 (1968).
Lax, P.D., Periodic Solutions of the KdV equation, in Lectures in Applied Mathematics, 15, A.C. Newell, ed. AMS, Providence, R.I. (1974).
Magnus, W., & W. Winkler, Hill's Equation. New York: Interscience Publishers 1966.
Miura, R.M., C.S. Gardner, & M.D. Kruskal, Korteweg-deVries equation and generalizations II. Existence of conservation laws and constants of the motion. J. Math. Phys. 9, 1204–1209 (1968).
Titchmarsh, E.C., Eigenfunction Expansions. Oxford: The Clarendon Press 1946.
Zaharov, V.E., & L.D. Faddeev, Korteweg-deVries equation: a completely integrable Hamiltonian system (in Russian). Funk. Anal. Prilož. 5, 18–27 (1971).
Goldberg, W., Bull. AMS. 80, 1111–1112 (1975).
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Communicated by M. Kac
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Flaschka, H. On the inverse problem for Hill's operator. Arch. Rational Mech. Anal. 59, 293–309 (1975). https://doi.org/10.1007/BF00250422
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DOI: https://doi.org/10.1007/BF00250422