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Nonlinear Equations and Inverse Spectral Problems on the Axis

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Operator Theory and Boundary Eigenvalue Problems

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 80))

Abstract

For a number of nonlinear equations the method of the inverse scattering problem [1]–[3] has led to a great progress in the investigation of the Cauchy problem on the axis (—∞ < ϰ < ∞). In the papers [4]–[6] the transition from the method of the scattering problem to the method of the inverse spectral problem was performed. It permitted to investigate some nonlinear equations on the half axis (0 ≤ ∞ < ∞).

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References

  1. Novikov S.P .(ed.) Theory of solitons, the inverse problem method. Moscow, Nauka, 1980.

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  3. Zakharov V.E., Shabat A.B. Applications of the inverse scattering method 1, Funct. Anal. Appl. 8, 3, 43–53, (1974).

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  4. Beresanskii Yu.M. Investigation of nonlinear difference equations by the inverse spectral problem method. Dokl. AN SSSR 281, 1, 16–19, (1985).

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  5. Sakhnovich L.A. Factorization problems and operator identities. Russian Math. Surv. 41, 1, 1–64, (1986).

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  7. Sakhnovich L.A. The hyperbolic sinus-Gordon equation. Izv. Vyssh. Uchebn. Zaved. Mat. 1, 54–63, (1991).

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Author information

Authors and Affiliations

  1. Pr. Dobrovolskogo 154 ap. 199, Odessa, 270111, Ukraine

    L. A. Sakhnovich

Authors
  1. L. A. Sakhnovich
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel Aviv University, 69978, Tel Aviv, Israel

    I. Gohberg

  2. Institut für Analysis, technische Mathematik und Versicherungsmathematik, TU Wien, 1040, Wien, Austria

    H. Langer

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© 1995 Birkhäuser Verlag Basel/Switzerland

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Sakhnovich, L.A. (1995). Nonlinear Equations and Inverse Spectral Problems on the Axis. In: Gohberg, I., Langer, H. (eds) Operator Theory and Boundary Eigenvalue Problems. Operator Theory: Advances and Applications, vol 80. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9106-6_14

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  • DOI: https://doi.org/10.1007/978-3-0348-9106-6_14

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9909-3

  • Online ISBN: 978-3-0348-9106-6

  • eBook Packages: Springer Book Archive

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