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The goal of this work is to study the existence of quasi-periodic solutionsin time to nonlinear beam equations with a multiplicative potential. Thenonlinearities are required to only finitely differentiable and the frequencyis along a pre-assigned direction. The result holds on any compact Lie group orhomogenous manifold with respect to a compact Lie group, which includes thestandard torus $\mathbf{T}^{d}$, the special orthogonal group $SO(d)$, thespecial unitary group $SU(d)$, the spheres $S^d$ and the real and complexGrassmannians. The proof is based on a differentiable Nash-Moser iterationscheme.

Quasi-periodic solutions to nonlinear beam equation on Compact Lie Groups with a multiplicative potential