On Quasitriviality and Integrability of a Class of Scalar Evolutionary   PDEs
  For certain class of perturbations of the equation $u_t=f(u) u_x$, we prove the existence of change of coordinates, called quasi-Miura transformations, that reduce these perturbed equations to the unperturbed ones. As an application, we propose a criterion for the integrability of these equations. 
Si-Qi Liu, Youjin Zhang