We consider the modified Witham equation ∂tv + ∂x √a² - ∂²x = ∂x (v³), (t; x) ∈ R x R; where pa2 √a² - ∂²x means the dispersion relation which correspond to nonlinear Kelvin and continental-shelf waves. We develop the factorization technique to study the large time asymptotics of solutions.