Skip to main content
SpringerLink
Log in

Spectral Theory of the Nonstationary Schrodinger Equation with a Two-Dimensionally Perturbed Arbitrary One-Dimensional Potential

  • Published:
Theoretical and Mathematical Physics Aims and scope Submit manuscript

Abstract

We consider the nonstationary Schrodinger equation with the potential being a perturbation of a generic one-dimensional potential by means of a decaying two-dimensional function in the framework of the extended resolvent approach. We give the corresponding modification of the Jost and advanced/retarded solutions and spectral data and present relations between them.

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

Similar content being viewed by others

REFERENCES

  1. B. B. Kadomtsev and V. I. Petviashvili, Sov. Phys. Dokl., 15, 539 (1970).

    Google Scholar 

  2. V. E. Zakharov and A. B. Shabat, Funct. Anal. Appl., 8, 226 (1974); V. S. Dryuma, JETP Letters, 19, 381 (1974).

    Article  Google Scholar 

  3. V. E. Zakharov and S. V. Manakov, Sov. Sci. Rev.: Phys. Rev., 1, 133 (1979); S. V. Manakov, Phys. D, 3, 420 (1981); A. S. Fokas and M. J. Ablowitz, Stud. Appl. Math., 69, 211 (1983); M. Boiti, J. Leon, and F. Pempinelli, Phys. Lett. A, 141, 96 (1989); Xin Zhou, Comm. Math. Phys., 128, 551 (1990); A. S. Fokas and L. Y. Sung, Math. Proc. Cambridge Philos. Soc., 125, 113 (1999).

    Google Scholar 

  4. M. Boiti, F. Pempinelli, A. K. Pogrebkov, and M. C. Polivanov, Theor. Math. Phys., 93, 1200 (1992); M. Boiti, F. Pempinelli, A. K. Pogrebkov, and M. C. Polivanov, Inverse Problems, 8, 331 (1992); M. Boiti, F. Pempinelli, and A. Pogrebkov, Inverse Problems, 10, 505 (1994); J. Math. Phys., 35, 4683 (1994); Theor. Math. Phys., 99, 511 (1994); “Spectral theory of solitons on a generic background for the KPI equation,” in: Nonlinear Physics: Theory and Experiment: Nature, Structure, and Properties of Nonlinear Phenomena (Proc. Workshop, Lecce, Italy, June 29–July 7, 1995, E. Alfinito, M. Boiti, L. Martina, and F. Pempinelli, eds.), World Scientific, Singapore (1996), p. 37; Inverse Problems, 13, L7 (1997); M. Boiti, F. Pempinelli, A. Pogrebkov, and B. Prinari, Theor. Math. Phys., 116, 3 (1998).

    Article  Google Scholar 

  5. A. S. Fokas and A. K. Pogrebkov, Nonlinearity, 16, 771 (2003).

    Article  Google Scholar 

  6. M. Boiti, F. Pempinelli, A. K. Pogrebkov, and B. Prinari, J. Math. Phys., 44, 3309 (2003).

    Article  Google Scholar 

  7. M. Boiti, F. Pempinelli, A. K. Pogrebkov, and B. Prinari, Proc. Steklov Math. Inst. (to appear).

  8. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method [in Russian], Nauka, Moscow (1980); English transl.: S. P. Novikov, S. V. Manakov, L. P. Pitaevskii, and V. E. Zakharov, Plenum, New York (1984); F. Calogero and A. Degasperis, Spectral Transform and Solitons: Tools to Solve and Investigate Nonlinear Evolution Equations, Vol. 1, North-Holland, Amsterdam (1982).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica, Universita di Lecce and Sezione INFN, Lecce, Italy

    M. Boiti, F. Pempinelli & B. Prinari

  2. Steklov Mathematical Institute, RAS, Gubkina St. 8, 119991, Moscow, Russia

    A. K. Pogrebkov

Authors
  1. M. Boiti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. Pempinelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. K. Pogrebkov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. B. Prinari
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 2, pp. 257–276, August, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Boiti, M., Pempinelli, F., Pogrebkov, A.K. et al. Spectral Theory of the Nonstationary Schrodinger Equation with a Two-Dimensionally Perturbed Arbitrary One-Dimensional Potential. Theor Math Phys 144, 1100–1116 (2005). https://doi.org/10.1007/s11232-005-0139-1

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11232-005-0139-1

Keywords

Search

Navigation