We study the one-dimensional nonlinear Klein-Gordon (NLKG) equation with a convolution potential, and we prove that solutions with small analytic norm remain small for exponentially long times. The result is uniform with respect to $c \geq 1$, which however has to belong to a set of large measure.
Solitons for the nonlinear Klein-Gordon equation
Instability of the standing waves for the nonlinear Klein-Gordon equations in one dimension
Long time behaviour of the nonlinear Klein-Gordon equation in the nonrelativistic limit, I
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