Skip to main content
SpringerLink
Log in

Algebrogeometric solutions of the nonlinear boundary problem on a segment for the sine-Gordon equation

  • Published:
Mathematical Notes Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Literature cited

  1. M. J. Ablowitz and H. Segur, “The inverse scattering transform: semi-infinite interval,” J. Math. Phys.,16, 1054–1056 (1975).

    Google Scholar 

  2. A. S. Focas, “An initial-boundary problem for the nonlinear Schrödinger equation,” Physica D,35, 167–185 (1989).

    Google Scholar 

  3. V. O. Tarasov, “Boundary problem for the nonlinear Schrödinger equation,” Zap. Nauchn. Semin. Leningr. Otdel. Mat. Inst.,169, 151–165 (1988).

    Google Scholar 

  4. I. T. Khabibullin, “Integrable initial-boundary problems,” Teor. Mat. Fiz.,86, No. 1, 43–52 (1991).

    Google Scholar 

  5. R. F. Bikbaev and V. O. Tarasov, “Initial-boundary problem for the nonlinear Schödinger equation,” J. Phys. A,24, No. 11, 2507–2517 (1991).

    Google Scholar 

  6. V. O. Tarasov, “The integrable initial-boundary value problem on a semiline: nonlinear Schrödinger and sine-Gordon equations,” Inv. Probl., No. 7, 435–449 (1991).

    Google Scholar 

  7. R. Parmentier, “Fluxions in distributions of Josephson contacts,” in: Soliton Effects [Russian translation], Mir, Moscow (1981), pp. 185–208.

    Google Scholar 

  8. E. K. Sklyanin, “Boundary conditions for integrable equations,” Funkts. Anal. Prilozh.,21, No. 2, 86–87 (1987).

    Google Scholar 

  9. R. F. Bikbaev and A. R. Its, “Algebrogeometric solutions of a boundary problem for the nonlinear Schrödinger equation,” Mat. Zametki,45, No. 5, 3–10 (1989).

    Google Scholar 

  10. R. F. Bikbaev, “Finite-zone solutions of boundary problems for integrable equations,” Mat. Zametki,48, No. 2, 10–18 (1990).

    Google Scholar 

  11. R. F. Bikbaev, “Integrable boundary problems and nonlinear Fourier harmonics,” Zap. Nauchn. Semin. Leningr. Otdel. Mat. Inst.,199, 23–30 (1992).

    Google Scholar 

  12. I. T. Khabibullin, “The Bäcklund transfer and initial-boundary problems,” Mat. Zametki,49, No. 4, 130–137 (1991).

    Google Scholar 

  13. R. F. Bikbaev and S. B. Kuksin, “Periodic boundary problem for the sine-Gordon equation, its small Hamiltonian perturbations, and the KAM-deformations of finite-zone tori,” Algeb. Anal.,4, No. 3, 70–111 (1992).

    Google Scholar 

  14. V. A. Kozel and V. P. Kotlyarov, “Almost-periodic solutions of the equation uxx−utt = sin u,” Dokl. Akad. Nauk UkrSSR,10A, 878–881 (1976).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. St. Petersburg Section, Steklov Mathematical Institute, Russian Academy of Sciences, USSR

    R. F. Bikbaev & A. R. Its

Authors
  1. R. F. Bikbaev
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. R. Its
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Matematicheskie Zametki, Vol. 52, No. 4, pp. 19–28, October, 1992.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bikbaev, R.F., Its, A.R. Algebrogeometric solutions of the nonlinear boundary problem on a segment for the sine-Gordon equation. Math Notes 52, 1005–1011 (1992). https://doi.org/10.1007/BF01210432

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01210432

Keywords

Search

Navigation