Bifurcations of self-similar solutions for reversing interfaces are studied in the
slow diffusion equation with strong absorption. The self-similar solutions bifurcate
from the time-independent solutions for standing interfaces. We show that such bifurcations
occur at particular points in parameter space (characterizing the exponents in the
diffusion and absorption terms) where the confluent hypergeometric functions satisfying
Kummer's differential equation truncate to finite polynomials. A two-scale asymptotic
method is employed to obtain the local dependencies of the self-similar reversing
interfaces near the bifurcation points. The asymptotic results are shown to be in
excellent agreement with numerical approximations of the self-similar solutions.
