Journal of Mathematical Sciences

, Volume 77, Issue 2, pp 3046–3050 | Cite as

Integrable boundary-value problems and nonlinear Fourier harmonics

  • R. F. Bikbaev


For the nonlinear Schrödinger equation, the integrable boundary-value problem on a segment is considered. The concept of nonlinear ϕ-harmonics similar to the ordinary Fourier harmonics in the linear case is suggested. A solution of the initial boundary-value problem on the semiaxis is constructed by means of reduction to the Cauchy problem on the whole axis. Bibliography: 11 titles.


Fourier Cauchy Problem Linear Case Fourier Harmonic 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    R. F. Bikbaev and A. R. It-s,Mat. Zametki,45, No. 5, 3 (1989).MathSciNetGoogle Scholar
  2. 2.
    R. F. Bikbaev,Mat. Zametki,48, No. 2, 10 (1990).MATHMathSciNetGoogle Scholar
  3. 3.
    R. F. Bikbaev and V. O. Tarasov,Algebra Analiz,3, No. 4, 77–91 (1991).MathSciNetGoogle Scholar
  4. 4.
    A. I. Bobenko,Zap. Nauchn. Semin. LOMI,179, 32 (1989).MATHGoogle Scholar
  5. 5.
    V. S. Vladimirov,Equations of Mathematical Physics [in Russian], Nauka, Moscow (1988).Google Scholar
  6. 6.
    J. Fay, “Theta-functions on Riemann surfaces,”Lect. Notes Math.,352 (1973).Google Scholar
  7. 7.
    G. Constabile, R. Parmentier, D. McLaughlin, and A. Scott,Appl. Phys. Lett.,32, 587 (1978).Google Scholar
  8. 8.
    E. D. Belokolos, A. I. Bobenko, V. B. Matveev, and V. Z. Enolskii,Uspekhi Mat. Nauk,41, No. 2, 3 (1986).MathSciNetGoogle Scholar
  9. 9.
    R. F. Bikbaev and V. O. Tarasov,J. Phys. A,24, 2507 (1991).CrossRefMathSciNetGoogle Scholar
  10. 10.
    L. A. Takhtadzhyan and L. D. Faddeev,Hamiltonian Approach in Soliton Theory [in Russian], Nauka, Moscow (1986).Google Scholar
  11. 11.
    I. Khabibullin,Teor. Mat. Fiz.,86, No. 1, 43 (1991).MATHMathSciNetGoogle Scholar

Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • R. F. Bikbaev

There are no affiliations available

Personalised recommendations