Period doubling solitons: yes or no?


Valkering, T.P. and Zeegers, Th. (1991) Period doubling solitons: yes or no? Physica D: Nonlinear phenomena, 51 (1-3). pp. 360-375. ISSN 0167-2789

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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.
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Copyright:© 1991 Elsevier Science
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