Whiskered quasi-periodic breathers for nonlinear Klein–Gordon chains with tangent potential

Abstract In this paper, we study whiskered quasi-periodic breathers for nonlinear Klein–Gordon chains with tangent potential or Maryland potential. Remarkably, nonlinear Klein–Gordon chains not only lose gauge invariance of the perturbation, but also they have infinite normally-hyperbolic directions. Using orthogonal transformation technique of linear operator and KAM iteration mechanism together with decay property of perturbation, we obtain the whiskered quasi-periodic breathers with positive measurable subset of spatial parameter.