1994/08/04 by Sergej Flach, S. Flach, Flach, S.
Computer Science · Physics and Astronomy · #Advanced Fiber Laser Technologies #Condensed Matter (cond-mat) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #cond-mat
paper · pdf · doi:10.48550/arxiv.cond-mat/9408014
Phys. Rev. E in press, LaTeX file, 5 figures available upon request, 20 pages, SF-7
arxiv created 1994/08/04 · openalex publication_date 1994/08/04 · arxiv updated 2009/11/30 · openalex created_date 2022/11/30 · openalex updated_date 2026/07/28
We use recent results that localized excitations in nonlinear Hamiltonian lattices can be viewed and described as multiple-frequency excitations. Their dynamics in phase space takes place on tori of corresponding dimension. For a one-dimensional Hamiltonian lattice with nearest neighbour interaction we transform the problem of solving the coupled differential equations of motion into a certain mapping Ml+1=F(Ml,Ml-1), where Ml for every l (lattice site) is a function defined on an infinite discrete space of the same dimension as the torus. We consider this mapping in the 'tails' of the localized excitation, i.e. for l → ± ∞. For a generic Hamiltonian lattice the thus linearized mapping is analyzed. We find conditions of existence of periodic (one-frequency) localized excitations as well as of multiple frequency excitations. The symmetries of the solutions are obtained. As a result we find that the existence of localized excitations can be a generic property of nonlinear Hamiltonian lattices in contrast to nonlinear Hamiltonian fields.