Travelling front solutions of a nonlocal Fisher equation

We consider a scalar reaction-diffusion equation containing a nonlocal term (an integral convolution in space) of which Fisher's equation is a particu lar case. We consider travelling wavefront solutions connecting the two uni form states of the equalion. We show that if the nonlocality is sufficientl y weak in a certain sense then such travelling fronts exist. We also constr uct expressions for the front and its evolution from initial data, showing that the main difference between our front and that of Fisher's equation is that for sufficiently strong nonlocality our front is non-monotone and has a very prominent hump.