For every c≥1, the 1D nonlinear Klein-Gordon equation with a convolution potential and small cubic nonlinearity admits linearly stable full-dimensional KAM tori with action decay e^{-2r ln^σ |n|}.
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The Existence of Full-Dimensional KAM tori for one-dimensional nonlinear Klein-Gordon equation
For every c≥1, the 1D nonlinear Klein-Gordon equation with a convolution potential and small cubic nonlinearity admits linearly stable full-dimensional KAM tori with action decay e^{-2r ln^σ |n|}.