Compactification of Patterns by a Singular Convection or Stress

A wide variety of propagating disturbances in physical systems are described by equations whose solutions lack a sharp propagating front. We demonstrate that presence of particular nonlinearities may induce such fronts. To exemplify this idea, we study both dissipative uₜ+ partial differentialₓf(u)=uₓₓ and dispersive uₜ+ partial differentialₓf(u)+uₓₓₓ=0 patterns, and show that a weakly singular convection f(u)=-u;{alpha}+u;{m}, 0<alpha<1