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Prog. Theor. Phys. Vol. 67 No. 5 (1982) pp. 1379-1395

[ Full Text PDF : FREE ACCESS (558K) ]

Impurity Localized Vibrational Mode of the Toda Lattice. I

— Perturbational Approach Based on the Inverse Scattering Method —

Fumio Yoshida and Tetsuro Sakuma

Department of Engineering Science, Hokkaido University, Sapporo 060

(Received January 16, 1982)

Abstract:

The impurity localized mode solutions of the Toda lattice are studied on the basis of the inverse scattering theory. Taking advantage of the N soliton solution formula, solutions for the surface and the bulk localized mode are obtained perturbatively up to the third order of the smallness parameter ε of the amplitude. For the surface impurity mode, our result agrees with that previously obtained by Nakamura. The solution for the bulk impurity mode is shown to have several properties similar to those in the surface impurity one, that is, temporal undamping of the vibration and frequency decreasing from the linear one with increasing amplitude.


URL : http://ptp.ipap.jp/link?PTP/67/1379/
DOI : 10.1143/PTP.67.1379

[ Full Text PDF : FREE ACCESS (558K) ] Citation:

References:

  1. A. Nakamura and S. Takeno, Prog. Theor. Phys. 58 (1977), 1074[PTP].
  2. A. Nakamura, Prog. Theor. Phys. 59 (1978), 1447[PTP].
  3. F. Yoshida and T. Sakuma, Prog. Theor. Phys. 60 (1978), 338[PTP].
  4. S. Watanabe and M. Toda, J. Phys. Soc. Jpn. 50 (1981), 3443[JPSJ].
  5. A. Nakamura, Prog. Theor. Phys. 61 (1979), 427[PTP].
  6. A. Nakamura and S. Takeno, Prog. Theor. Phys. 62 (1979), 33[PTP].
  7. N. Yajima, Physica Scripta 20 (1979), 431.
  8. M. Toda, Theory of Nonlinear Lattices (Springer-Verlag N.Y. 1981).
  9. E. Date and S. Tanaka, Prog. Theor. Phys. 55 (1976), 457[PTP].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 58 (1989) pp. 1539-1549 :
    Impurity Localized Modes of Nonlinear Lattice Systems
    Katsufumi Nagahama and Nobuo Yajima
  2. Journal of the Physical Society of Japan 61 (1992) pp. 1505-1511 :
    Undamping of Localized Mode Vibrations in a Nonlinear Diatomic Lattice
    Masanori Aoki
  3. Journal of the Physical Society of Japan 61 (1992) pp. 4344-4349 :
    Scattering of Envelope Solitons by a Mass Impurity in Nonlinear Lattices
    Takeshi Iizuka and Miki Wadati
  4. Journal of the Physical Society of Japan 62 (1993) pp. 1932-1938 :
    Soliton Scattering Due to a Heavy Impurity in Nonlinear Lattice
    Takeshi Iizuka and Miki Wadati
  5. Journal of the Physical Society of Japan 63 (1994) pp. 466-471 :
    Internal-Mode-Induced Resonances in Soliton-Impurity Interactions
    Fei Zhang, Yuri S. Kivshar and Luis Vázquez
  6. Progress of Theoretical Physics Vol. 68 No. 1 (1982) pp. 29-36 :
    Impurity Localized Vibrational Mode of the Toda Lattice. II
    Fumio Yoshida and Tetsuro Sakuma

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