  In this work we present an analytical and numerical study of rogue and
solitary waves in a coupled one-dimensional nonlinear lattice that involves
both axial and rotational degrees of freedom. Using a multiple-scale analysis
we derive a system of coupled nonlinear Schr\"odinger type equations in order
to approximate solitary waves and rogue waves of the coupled lattice model.
Numerical simulations are found to agree with the analytical approximations. We
also consider generic initialization data in the form of a Gaussian profile and
observe that they can result in the spontaneous formation of rogue wave-like
patterns in the lattice. The solitary and rogue waves in the lattice
demonstrate both energy isolation and exchange between the axial and rotational
degrees of freedom of the system. This suggests that the studied coupled
lattice has the potential to be an efficient energy isolation, transfer, and
focusing medium.
