  We study a pressureless Euler system with a nonlinear density-dependent
alignment term, originating in the Cucker-Smale swarming models. The alignment
term is dissipative in the sense that it tends to equilibrate the velocities.
Its density dependence is natural: the alignment rate increases in the areas of
high density due to species discomfort. The diffusive term has the order of a
fractional Laplacian $(-\partial_{xx})^{\alpha/2}$, $\alpha \in (0, 1)$. The
corresponding Burgers equation with a linear dissipation of this type develops
shocks in a finite time. We show that the alignment nonlinearity enhances the
dissipation, and the solutions are globally regular for all $\alpha \in (0,
1)$. To the best of our knowledge, this is the first example of such
regularization due to the non-local nonlinear modulation of dissipation.
