Recurrence phenomena in soliton propagation in a lattice with impurities
- 7 March 1988
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 21 (5) , 1253-1270
- https://doi.org/10.1088/0305-4470/21/5/020
Abstract
The scattering of a soliton from a mass impurity in a Morse or Toda one-dimensional lattice with periodic boundary conditions is studied numerically. The energy of the soliton as a function of time exhibits either a fast decay (chaotic behaviour) or a recurrence, or an intermediate 'metastable' behaviour, which consists of a time period when recurrence takes place, followed by a fast decay. A model is developed to explain the recurrence and predict the recurrence time. A semiquantitative argument is also presented to explain the 'metastable' case. Finally the generality of this type of behaviour is discussed.Keywords
This publication has 22 references indexed in Scilit:
- Chaos upon soliton decay in a perturbed periodic toda chainPhysica D: Nonlinear Phenomena, 1986
- Kink, breather and asymmetric envelope or dark solitons in nonlinear chains. I. Monatomic chainJournal of Physics C: Solid State Physics, 1985
- Boltzmann's ultraviolet cutoff and Nekhoroshev's theorem on Arnold diffusionNature, 1984
- Instability and confined chaos in a nonlinear dispersive wave systemPhysics of Fluids, 1982
- Nonlinear normal modes for the Toda ChainJournal of Computational Physics, 1982
- The Toda lattice. II. Existence of integralsPhysical Review B, 1974
- Integrals of the Toda latticePhysical Review B, 1974
- The applicability of the third integral of motion: Some numerical experimentsThe Astronomical Journal, 1964
- PROOF OF A THEOREM OF A. N. KOLMOGOROV ON THE INVARIANCE OF QUASI-PERIODIC MOTIONS UNDER SMALL PERTURBATIONS OF THE HAMILTONIANRussian Mathematical Surveys, 1963
- Equipartition of Energy for Nonlinear SystemsJournal of Mathematical Physics, 1961