  The transverse Nernst Ettingshausen (N-E) effect and electron mobility in
Pb$_{1-x}$Sn$_x$Se alloys are studied experimentally and theoretically as
functions of temperature and chemical composition in the vicinity of vanishing
energy gap $E_g$. The study is motivated by the recent discovery that, by
lowering the temperature, one can change the band ordering from trivial to
nontrivial one in which the topological crystalline insulator states appear at
the surface. Our work presents several new aspects. It is shown experimentally
and theoretically that the bulk N-E effect has a maximum when the energy gap
$E_g$ of the mixed crystal goes through zero value. This result contradicts the
claim made in the literature that the N-E effect changes sign when the gap
vanishes. We successfully describe $dc$ transport effects in the situation of
extreme band's nonparabolicity which, to the best of our knowledge, has never
been tried before. A situation is reached in which both two-dimensional bands
(topological surface states) and three-dimensional bands are linear in electron
\textbf{k} vector. Various scattering modes and their contribution to transport
phenomena in Pb$_{1-x}$Sn$_x$Se are analyzed. As the energy gap goes through
zero, some transport integrals have a singular (nonphysical) behaviour and we
demonstrate how to deal with this problem by introducing damping.
