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Prog. Theor. Phys. Supplement No.45 (1970) pp. 201-208

[ Full Text PDF : FREE ACCESS (588K) ]

On the Stability of Lattice Solitons

Naotake Ooyama and Nobuhiko Saitô

Department of Applied Physics, Waseda University, Tokyo

Abstract:

The stability of lattice solitons is examined on computer. The three-body collision is found to preserve the initial identity of individual solitons participating the three-body collision. Large deformation provokes a soliton to split into two solitons and a train of ripples. The stability of solitons under random disturbances is examined on computer. The speed of a soliton decreases gradually when large disturbance is given initially on the medium, and thus the soliton is subjected a viscous damping. Furher it is surmised from the experiments that there exists a critical value of the energy of the disturbance given to the medium, under which the soliton is stable and the speed is not affected by the presence of the disburbance.


URL : http://ptp.ipap.jp/link?PTPS/45/201/
DOI : 10.1143/PTPS.45.201

[ Full Text PDF : FREE ACCESS (588K) ] Citation:

References:

  1. M. Toda, J. Phys. Soc. Jpn. 22 (1967), 431[JPSJ]; ibid. 23 (1967), 501[JPSJ]; Prog. Theor. Phys. Suppl. No. 45 (1970), 174[PTP].
  2. N. J. Zabusky and M. D. Kruskal, Phys. Rev. Lett. 15 (1965), 240[APS]; Nonlinear Partial Differential Equations, edited by W. F. Ames (Acad. Press., New York, 1967), p. 223.
  3. P. D. Lax, Commun. Pure Appl. Math. 21 (1968), 467-490.
  4. M. Toda, Proceedings of the International Conference on Statistical Mechanics, Kyoto, 1968, J. Phys. Soc. Jpn. 26 (1969) Suppl., p. 235.
  5. E. Fermi, J. Pasta and S. Ulam, Los Alamos Scientific Laboratory Report LA-1940 (1955).
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    N. Ooyama, H. Hirooka and N. Saitô, J. Phys. Soc. Jpn. 27 (1969), 815[JPSJ].
  7. N. Saitô, H. Hirooka, N. Ooyama and Y. Aizawa, Prog. Theor. Phys. Suppl. No. 45 (1970), 209[PTP].

Citing Article(s) :

  1. Journal of the Physical Society of Japan 59 (1990) pp. 1571-1580 :
    Localized Modes in the Long-Time Behavior of Anharmonic Lattices
    Shozo Takeno
  2. Progress of Theoretical Physics Vol. 50 No. 5 (1973) pp. 1547-1560 :
    On the Integrability of the Toda Lattice
    Joseph Ford, Spotswood D. Stoddard and Jack S. Turner
  3. Progress of Theoretical Physics Supplement No.59 (1976) pp. 64-100 :
    A Variety of Nonlinear Network Equations Generated from the Bäcklund Transformation for the Toda Lattice
    Ryogo Hirota and Junkichi Satsuma

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