Localized Excitations in Discrete Hamiltonian Systems

  • Sergej Flach
  • Charles R. Willis
Part of the NATO ASI Series book series (NSSB, volume 329)


The modification of soliton properties (e. g. of kinks and breathers) in discrete systems has been studied over a rather long period of time1. Recently Takeno2 has discussed a new type of nonlinear localized excitations (NLE) in one-dimensional discrete lattices. Despite the fact that the existence of NLE was confirmed by computer simulations and approximate one-frequency solutions for the NLE could be found (Q l (t) = Q l (t + 2π/ω1), where Q l is the l-th particle displacement from the ground state position), the reason for the existence of the NLE remained unclear.


Central Particle Infinite System Localize Excitation Reduce Problem Chaotic Trajectory 
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  1. 1.
    A.R. Bishop, G. Grüner and B. Nicolaenko (ed). “Spatio-Temporal Coherence and Chaos in Physical Systems”, North-Holland Physics Publishing, Amsterdam (1986).MATHGoogle Scholar
  2. 2.
    S. Takeno, Theory of stationary anharmonic localized modes in solids, J.Phys.Soc.Japan 61:2821(1992).ADSCrossRefGoogle Scholar
  3. 3.
    S. Flach and C.R. Willis, Localized excitations in a discrete Klein-Gordon system, Phys. Lett. A, submitted to.Google Scholar
  4. 4.
    S. Flach and C.R. Willis, Properties of localized excitations in 1D discrete systems, this volume.Google Scholar

Copyright information

© Springer Science+Business Media New York 1994

Authors and Affiliations

  • Sergej Flach
    • 1
  • Charles R. Willis
    • 1
  1. 1.Department of PhysicsBoston UniversityBostonUSA

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