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Difference Schrödinger equation and quasisymmetric polynomials

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Abstract

We study the singularity of solutions of the Schrödinger equation with a finite potential at the point k = 0. In the case of delta-type potentials, we show that the nature of this singularity is automodel in a certain sense. We discuss using the obtained results to construct an approximate solution of the inverse scattering problem on the whole axis. For this, we introduce the concept of a quasisymmetric polynomial associated with a given curve.

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References

  1. A. B. Shabat, Theor. Math. Phys., 183, 540–552 (2015).

    Article  Google Scholar 

  2. B. Levin, Lectures on Entire Functions, Amer. Math. Soc., New York (1996).

    MATH  Google Scholar 

  3. A. Povzner, Mat. Sb., n.s., 23(65), No. 1, 3–52 (1948).

    MathSciNet  Google Scholar 

  4. A. B. Shabat, Funct. Anal. Appl., 9, 244–247 (1975).

    Article  Google Scholar 

  5. U. V. Barkina and S. N. Melikhov, Vladikavkaz. Mat. Zh., 16, No. 4, 27–40 (2014).

    Google Scholar 

  6. A. B. Shabat, Theor. Math. Phys., 179, 637–648 (2014).

    Article  MATH  MathSciNet  Google Scholar 

  7. B. A. Dubrovin, V. B. Matveev, and S. P. Novikov, Russ. Math. Surveys, 31, 59–146 (1976).

    Article  MATH  MathSciNet  ADS  Google Scholar 

  8. E. Korotyaev, Inverse Problems, 21, 325–341 (2005).

    Article  MATH  MathSciNet  ADS  Google Scholar 

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Authors and Affiliations

  1. Landau Institute for Theoretical Physics, RAS, Moscow, Russia

    A. B. Shabat

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  1. A. B. Shabat
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Correspondence to A. B. Shabat.

Additional information

Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 184, No. 2, pp. 200–211, August, 2015.

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Shabat, A.B. Difference Schrödinger equation and quasisymmetric polynomials. Theor Math Phys 184, 1067–1077 (2015). https://doi.org/10.1007/s11232-015-0318-7

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  • DOI: https://doi.org/10.1007/s11232-015-0318-7

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