  Reaction-diffusion equations with a nonlinear source have been widely used to
model various systems, with particular application to biology. Here, we provide
a solution technique for these types of equations in $N$-dimensions. The
nonclassical symmetry method leads to a single relationship between the
nonlinear diffusion coefficient and the nonlinear reaction term; the subsequent
solutions for the Kirchhoff variable are exponential in time (either growth or
decay) and satisfy the linear Helmholtz equation in space. Example solutions
are given in two dimensions for particular parameter sets for both quadratic
and cubic reaction terms.
