Skip to main content
Log in

Scattering data for the nonstationary Dirac equation

  • Published:
Journal of Soviet Mathematics Aims and scope Submit manuscript

Abstract

The existence of indeterminacy in the choice of scattering data for the auxiliary linear system for the Davey-Stewartson I-equation is noted. A connection is established between different scattering data and the corresponding conjugation matrix for the nonlocal Riemann problem.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Literature cited

  1. L. A. Takhtadzgyan and L. D. Faddeev, Hamiltonian Approach to the Theory of Solitons [in Russian], Nauka, Moscow (1986).

    Google Scholar 

  2. A. G. Reiman and M. A. Semenov-Tyan-Shanskii, “Hamiltonian structure of Kadomtsev-Petviashvili type equations,” J. Sov. Math.,31, No. 6 (1985).

  3. L. P. Nizhnik and M. D. Pochiniiko, “Spatially two-dimensional nonlinear Schrödinger equation as an integrable Hamiltonian system,” Preprint 85-24, Inst. Mat. Akad. Nauk USSR, Kiev (1985).

    Google Scholar 

  4. V. D. Lipovskii, “Hamiltonian structure of Kadomtsev-Petviashvili equation II in the class of decreasing Cauchy data,” Funkts. Anal. Prilozhen.,20, No. 4, 35–45 (1986).

    Google Scholar 

  5. P. P. Kulish and V. D. Lipovskii, “Hamiltonian interpretation of the method of the inverse problem for the Davey-Stewartson equation,” J. Sov. Math.,46, No. 5 (1989).

  6. V. D. Lipovskii, “Hamiltonian approach to the Davy-Stewartson equation II,” Vestn. Leningr. Gos. Univ. (LGU), Ser. Fiz. Khim., No. 4, 67–70 (1987).

    Google Scholar 

  7. Z. Jiang, R. K. Bullough, and S. V. Manakov, “Complete integrability of the KP equations in 2+1 dimensions,” Physica D,18, 305–307 (1986).

    MathSciNet  Google Scholar 

  8. Z. Jiang, “Integrable system and integrability,” Ph. D. thesis. Manchester UMIST, 1987.

  9. C. L. Schultz, M. J. Ablowitz, D. Bar Yaacov, “Davey-Stewartson I — A quantum 2+1 dimensional integrable system,” Preprint, Clarkson University, Potsdam, USA, 1987.

    Google Scholar 

  10. S. V. Manakov, “The inverse scattering transform for the time-dependent Schrödinger equation and Kadomtsev-Petviashvili equation,” Physica D,3, 420–427 (1981).

    Google Scholar 

  11. A. S. Fokas and M. J. Ablowitz, “On the inverse scattering transform of multidimensional nonlinear equations,” J. Math. Phys.,25, 2494–2505 (1984).

    Google Scholar 

  12. L. D. Faddeev, “Inverse problem of quantum theory of scattering,” in: Current Problems of Mathematics [in Russian], Vol. 3, Vsesoyuz. Inst. Nauk. Tekh. Inform. (VINITI), Moscow (1974), pp. 93–180.

    Google Scholar 

Download references

Authors

Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 164, pp. 170–175, 1987.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kulish, P.P., Lipovskii, V.D. & Shirokov, A.V. Scattering data for the nonstationary Dirac equation. J Math Sci 47, 2488–2492 (1989). https://doi.org/10.1007/BF01840430

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01840430

Keywords

Navigation