  We report localized and unidirectional nonlinear traveling edge waves
discovered theoretically and numerically in a 2D mechanical (phononic)
topological insulator. The lattice consists of a collection of pendula with
weak Duffing nonlinearity connected by linear springs. We show that the
classical 1D nonlinear Schrodinger equation governs the envelope of 2D edge
modes, and study the propagation of traveling waves and rogue waves in 1D as
edge solitons in 2D. As a result of topological protection, these edge solitons
persist over long time intervals and through irregular boundaries.
