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Darboux transformation and two-dimensional Toda lattice

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Abstract

The Darboux transformation method is used to construct multisoliton solutions of an infinite two-dimensional Toda lattice, which depend on an arbitrary number of functional parameters.

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Literature cited

  1. I. M. Krichever, “Algebraic curves and nonlinear difference equations,” Usp. Mat. Nauk,33, No. 4(202), 215–216 (1978).

    Google Scholar 

  2. V. B. Matveev, “Darboux transformation and the explicit solutions of differential-difference and difference-difference evolution equations. I,” Lett. Math. Phys.,3, 217–222 (1979).

    Google Scholar 

  3. V. B. Matveev and M. A. Salle, “Differential-difference evolution equations. II (Darboux transformation for the Toda lattice),” Lett. Math. Phys.,3, 425–429 (1979).

    Google Scholar 

  4. E. Date, “On a direct method of constructing multisoliton solutions,” Proc. Jpn. Acad. Ser. A, Math. Sci.,55, No. 1, 27–30 (1979).

    Google Scholar 

  5. A. V. Mikhailov (Mikchailov), Proceedings of the Soviet-American Workshop on Solitons, Kiev, 1979, North-Holland, Amsterdam (in press).

    Google Scholar 

  6. A. N. Leznov and M. V. Saveliev, “Representation of zero curvature for the system of nonlinear partial differential equations\(x_{\alpha ,z\overline z } = \exp (kx)_\alpha \), and its integrability,” Lett. Math. Phys.,3, 489–494 (1979).

    Google Scholar 

  7. F. R. Gantmakher and M. G. Krein, Oscillation Matrices and Kernels and Small Vibrations of Mechanical Systems [in Russian], 2nd ed., Gostekhteorlitizdat, Moscow (1950).

    Google Scholar 

  8. P. Hartman, “Difference equations: disconjugacy, principal solutions, Green's functions, complete monotonicity,” Trans. Am. Math. Soc.,246, No. 523, 1–30 (1978).

    Google Scholar 

  9. V. I. Volterra, Leçons sur la Théorie Mathématique de la Lutte pour La Vie, Gauthier-Villars et Cie., Paris (1931).

    Google Scholar 

  10. Yu. M. Svirezhev and D. O. Logofet, Stability of Biological Associations [in Russian], Nauka, Moscow (1978).

    Google Scholar 

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Authors
  1. V. B. Matveev
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  2. M. A. Salle
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Additional information

Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 101, pp. 111–118, 1981.

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Matveev, V.B., Salle, M.A. Darboux transformation and two-dimensional Toda lattice. J Math Sci 23, 2441–2446 (1983). https://doi.org/10.1007/BF01084172

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  • DOI: https://doi.org/10.1007/BF01084172

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