  A class of the Newell-Whitehead-Segel equations (also known as generalized
Fisher equations and Newell-Whitehead equations) is studied with Lie and
"nonclassical" symmetry points of view. The classifications of Lie reduction
operators and of regular nonclassical reduction operators are performed. The
set of admissible transformations (the equivalence groupoid) of the class is
described exhaustively. The criterion of reducibility of variable coefficient
Newell-Whitehead-Segel equations to their constant coefficient counterparts is
derived. Wide families of exact solutions for such variable coefficient
equations are constructed.
