Distributional solutions of Burgers' equation and intrinsic regular graphs in Heisenberg groups

In the present paper we will characterize the continuous distributional solutions of Burgers' equation as those which induce intrinsic regular graphs in the first Heisenberg group H¹≡R³, endowed with a left-invariant metric d_∞ equivalent to its Carnot-Carathéodory metric. We will also extend the characterization to higher Heisenberg groups Hn≡R2n+1.