Publication: Soliton-radiation interaction in nonlinear integrable lattices
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1987-07-15
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Amer Physical Soc
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Abstract
The effect of the radiation modes on soliton motion in nonlinear lattices is investigated. A method based on the inverse scattering transform is developed, which enables us to characterize the position shifts of solitons due to their interaction with the radiation component. Applications to the Toda and
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©Amer Physical Soc.
It is a pleasure to thank Professor P. C. Sabatier and the group of the Laboratoire de Physique Mathematique of Montpellier University for warm hospitality while this work was in progress. Partial financial support from the Comision Asesora de Investigacion Cientifica y Tecnica, Spain is also acknowledged.
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1. M. Toda, Theory of Nonlinear Lattices (Springer, Berlin, 1981).
2. M. J. Ablowitz and H. Segur, Solitons and the Inoerse Scattering Transform (SIAM, Philadelphia, 1981).
3. B. A. Kupershmidt, Discrete Lax Equations and Differential Difference Calculus, Asterisque 123 (Societe Mathematique de France, Paris, 1985).
4. N. Theodorakopoulos, in Dynamical Problems in Soliton Systems, proceedings of the Seventh Kyoto Summer Institute, edited by S. Takeno (Springer, Berlin, 1985).
5. L. Martinez Alonso, Phys. Rev. D 32, 1459 (1985).
6. S. V. Manakov, Zh. Eksp. Teor. Fiz. 67, 543 (1974) [Sov. Phys. JETP 40, 269 (1975)].
7. V. E. Zakharov, S. V. Manakov, S. P. Novikov, and L. P. Pitaevskii, Theory of Solitons: The Inverse Scattering Method (Pl, N Y k, 1984).
8. For a treatment of truncated asymptotic solutions and their applications to a continuous system, see L. MartÃnez Alonso, Phys. Lett. 112A, 361 (1985).
9. This condition is always satisfied by those members of the Toda hierarchy for which the integer M in Eq. (2.15) is even. In particular, it holds for the Toda lattice.
10. N. Theodorakopoulos and F. G. Mertens, Phys. Rev. B 28, 3512 (1983).
11. This equation is obtained by setting z =k^1 in Eq. (2.5) of Ref. 7, p. 52.