Geodesic
Soliton dynamics for near integrable differential-difference equations
Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 315-321 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this talk, we consider both the spectral and the direct perturbation methods for studying perturbations an integrable differential-difference equation, the Toda lattice. Both methods employ the formalism of inverse scattering to represent the corrections in terms of an appropriate basis of squared eigenfunctions. 
@article{TMF_1994_99_2_a18,
     author = {Russell L. Herman},
     title = {Soliton dynamics for near integrable differential-difference equations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {315--321},
     year = {1994},
     volume = {99},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a18/}
}
TY  - JOUR
AU  - Russell L. Herman
TI  - Soliton dynamics for near integrable differential-difference equations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 1994
SP  - 315
EP  - 321
VL  - 99
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a18/
LA  - en
ID  - TMF_1994_99_2_a18
ER  - 
%0 Journal Article
%A Russell L. Herman
%T Soliton dynamics for near integrable differential-difference equations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 1994
%P 315-321
%V 99
%N 2
%U http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a18/
%G en
%F TMF_1994_99_2_a18
Russell L. Herman. Soliton dynamics for near integrable differential-difference equations. Teoretičeskaâ i matematičeskaâ fizika, Tome 99 (1994) no. 2, pp. 315-321. http://geodesic.mathdoc.fr/item/TMF_1994_99_2_a18/

[1] Flaschka H., “On the Toda Lattice II. Inverse Scattering Solutions”, Prog. Theor. Phys., 55 (1974), 438–456 | DOI | MR

[2] Herman R. L., “Resolution of the motion of a perturbed KdV soliton”, Inverse Problems, 6 (1990), 43–54 | DOI | MR | Zbl

[3] Herman R. L., “A Direct Approach to Studying Soliton Perturbations”, J. Phys. A, 23 (1990), 2327–2362 | DOI | MR | Zbl

[4] Kako F., “Propagation of solitons in a dissipative nonlinear transmission line”, J. Phys. Soc. Jpn., 47 (1979), 1686–1692 | DOI | MR

[5] Karpman V. I., Maslov E. M., “Structure of Tails Produced under the Action of Perturbations of Solitons”, Sov. Phys. JETP, 48 (1978), 252–258 | MR

[6] Kaup D. J., “A perturbation expansion for the Zakharov–Shabat inverse scattering transform”, SIAM J. Appl. Math., 31 (1976), 121–133 | DOI | MR | Zbl

[7] Kaup D. J., Newell A. C., “Solitons as Particles, Oscillators, and in Slowly Changing Media: A Singular Perturbation Theory”, Proc. Roy. Soc. Lond. A, 361 (1978), 413–446 | DOI | MR

[8] Keener J. P., McLaughlin D. W., “Solitons Under Perturbations”, Phys. Rev. A, 16 (1977), 777–790 | DOI | MR

[9] Kusela T., Hietarinta J., “Numerical, Experimental and Analytical Studies of the Dissipative Toda Lattice I. The Behaviour of a Single Solitary Wave”, Physica D, 41 (1990), 322 | DOI | MR

[10] Nagashimi H., Amagishi Y., “Experiment on the Toda Lattice Using Nonlinear Transmission Lines”, J. Phys. Soc. Jpn., 45 (1978), 680–688 | DOI

[11] Toda M., Theory of Nonlinear Lattices, Springer-Verlag, 1981 | MR | Zbl

[12] Washimi H., Tanuiti T., “Propagation of Ion-acoustic Solitary Waves of Small Amplitude”, Phys. Rev. Lett., 17 (1966), 996–998 | DOI

[13] Yajima N., “Scattering of Lattice Solitons from a Mass Impurity”, Phys. Scrip., 20 (1979), 431–434 | DOI