Topology in Nonlinear Mechanical Systems

Many advancements have been made in the field of topological mechanics. The majority works, however, concerns invariant a linear theory. We, this work, present generic prescription defining indices which accommodates non-linear effects mechanical systems without taking any approximation. Invoking tools differential geometry, Z-valued quantity terms Poincare-Hopf index, that features zero modes (ZMs), is predicted. We further identify one type topologically protected solitons are robust to disorders. Our constitutes new direction searching for novel ZMs future.