  We consider quasi-stationary (travelling wave type) solutions to a general
nonlinear reaction-convection-diffusion equation with arbitrary, autonomous
coefficients. The second order nonlinear equation describing one dimensional
travelling waves can be reduced to a first kind first order Abel type
differential equation By using two integrability conditions for the Abel
equation (the Chiellini lemma and the Lemke transformation), several classes of
exact travelling wave solutions of the general reaction--convection-diffusion
equation are obtained, corresponding to different functional relations imposed
between the diffusion, convection and reaction functions. In particular, we
obtain travelling wave solutions for two non-linear second order partial
differential equations, representing generalizations of the standard diffusion
equation and of the classical Fisher--Kolmogorov equation, to which they reduce
for some limiting values of the model parameters. The models correspond to some
specific, power law type choices of the reaction and convection functions,
respectively. The travelling wave solutions of these two classes of
differential equations are investigated in detail by using both numerical and
semi-analytical methods.
