Nonlinear mode phenomenology for sine-Gordon breather excitations

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Abstract
Hamiltonians in one space dimension of the phi -four and sine-Gordon classes are considered, emphasising kink- and breather-like excitations. A calculation of classical dynamic structure factors based on a kink ideal gas phenomenology is reviewed in terms of the 'central peaks' predicted. This phenomenological scheme is extended to include breather excitations. It is suggested that, for correlations of appropriate functions, the breather excitations can give rise to a low-frequency ('central') response from their particle-like envelope and a high-frequency response from their internal oscillatory motions in qualitative accord with molecular dynamics simulations.