  We present a complete description of the similarity solutions
$u_{\alpha}(x,t)=t^{-\alpha/2}f(\Vert x \Vert/\sqrt{t};\alpha)$ for the
following nonlinear diffusion equation $$ u_{t}+\gamma\vert u_{t} \vert =\Delta
u\qquad(-1<\gamma<1) $$ The behaviors of these solutions are obtained through
the explicit representation of $f(\eta;\alpha)$, in terms of Kummer and Tricomi
functions. Considering results about confluent hypergeometric functions, new
methods to describe asymptotic and oscillatory behaviors of the similarity
solutions are obtained. We prove that there exists an increasing and unbounded
sequence of positive similarity exponents such that the associated profile $f$
has a gaussian rate decay. These special similarity exponents are related with
the zeros of Kummer and Tricomi functions. Finally, we indicate how to extend
our results on more general nonlinear diffusion equations.

Analysis of PDEs