Author:

Keywords:

population dynamics, reaction-diffusion equation, exact solutions, Science & Technology, Physical Sciences, Physics, Multidisciplinary, Physics, Mathematical, Physics, FISHER EQUATION, 01 Mathematical Sciences, 02 Physical Sciences, Mathematical Physics, 49 Mathematical sciences, 51 Physical sciences

Abstract:

© 2017 IOP Publishing Ltd. Physically motivated modified Fisher equations are studied in which nonlinear convection and nonlinear diffusion is allowed for besides the usual growth and spread of a population. It is pointed out that in a large variety of cases separable functions in the form of exponentially decaying sharp wavefronts solve the differential equation exactly provided a co-moving point source or sink is active at the wavefront. The velocity dispersion and front steepness may differ from those of some previously studied exact smooth traveling wave solutions. For an extension of the reaction-diffusion-convection equation, featuring a memory effect in the form of a maturity delay for growth and spread, also smooth exact wavefront solutions are obtained. The stability of the solutions is verified analytically and numerically.