The linear response theory of the one dimensional nonlinear systems is formulated in the limit of the overdamping. Transfer integral method is applied to investigate the dynamical structure factor S (k =0, ω). The equation of motion for the distribution function is reduced to a set of independent equations for normal modes. As an example the structure factor for the φ4 chain is calculated to be the sum of a very narrow central peak and a broad overdamped phonon peak. The origin of the former is supposed to be the domain wall motion.
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