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Explicit solutions of an integrable boundary value problem for the two-dimensional toda lattice

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Abstract

We obtain an explicit solution of the integrable boundary value problem for the two-dimensional Toda lattice using the inverse scattering method. We interpret the integrability property in terms of the corresponding linear problem, the Gel’fand-Levitan-Marchenko equation, and the dressing procedure. The simplest initial solutions of the boundary value problem become new nontrivial solutions after the dressing procedure is applied.

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References

  1. A. V. Mikhailov, JETP Lett., 30, 414–418 (1979).

    ADS  Google Scholar 

  2. A. V. Mikhailov, Phys. D, 3, 73–117 (1981).

    Article  MATH  Google Scholar 

  3. A. Nakamura, J. Phys. Soc. Japan, 52, 380–387 (1983).

    Article  MathSciNet  ADS  Google Scholar 

  4. M. V. Babich, V. B. Matveev, and M. A. Sail’, “A binary Darboux transform for the Toda lattice,” J. Math. Sci. (New York), 35, 2582–2589 (1986).

    Article  MATH  Google Scholar 

  5. I. T. Khabibullin and E. V. Gudkova, Funct. Anal. Appl., 38, 138–148 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  6. M. Gürses, I. T. Habibullin, and K. Zheltukhin, J. Math. Phys., 48, 102702 (2007).

    Article  MathSciNet  ADS  Google Scholar 

  7. V. É. Adler, I. T. Habibullin, and A. B. Shabat, Theor. Math. Phys., 110, 78–90 (1997).

    Article  MATH  Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics with Computing Center, Ufa Science Center, RAS, Ufa, Russia

    V. L. Vereshchagin

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  1. V. L. Vereshchagin
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Correspondence to V. L. Vereshchagin.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 165, No. 1, pp. 25–31, October, 2010.

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Vereshchagin, V.L. Explicit solutions of an integrable boundary value problem for the two-dimensional toda lattice. Theor Math Phys 165, 1256–1261 (2010). https://doi.org/10.1007/s11232-010-0107-2

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  • DOI: https://doi.org/10.1007/s11232-010-0107-2

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