Period doubling solitons: yes or no?

T.P. Valkering, T.W.P. Zeegers, Th. Zeegers

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    Abstract

    We investigate the possibility of period doubling transition to temporal chaos of a coherent structure in a finite dimensional Hamiltonian system with moderately small friction. A solitary wave in a periodically driven chain of particles provides a typical example. To this end the equations of motion are transformed to those of one driven dominant oscillator with one degree of freedom, weakly coupled to a set of oscillators representing the other degrees of freedom. The equations for the dominant oscillator alone confirm the possibility of such a transition to chaos for well chosen driving. However, taking into account coupling to the other degrees of freedom, one must conclude that the supposed infinite period doubling sequence for small or no dampling survives only in a heavily damaged state. In practice a reproducable completed sequence cannot be expected unless the damping is strong enough.
    Original languageUndefined
    Pages (from-to)360-375
    Number of pages15
    JournalPhysica D
    Volume51
    Issue number1-3
    DOIs
    Publication statusPublished - 1991

    Keywords

    • IR-24794
    • METIS-129595

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