A Nekhoroshev type theorem for the nonlinear Klein-Gordon equation with potential

TL;DR

This paper proves that solutions to a one-dimensional nonlinear Klein-Gordon equation with a convolution potential stay small for exponentially long times, uniformly for large measure sets of the parameter c.

Contribution

It establishes a Nekhoroshev type theorem for the NLKG with potential, demonstrating long-time stability in the small analytic norm regime.

Findings

Solutions remain small for exponentially long times

Uniform stability result with respect to parameter c

Applicable for large measure sets of c

Abstract

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.