Lie point symmetries, conservation laws, and solutions of a space dependent reaction–diffusion equation

We find the Lie point symmetries of a nonlinear population model, i.e. a second-order reaction-diffusion equation with a variable coefficient b ( x ) and classify the model into three kinds. Then, with the help of the Lie point symmetries and self-adjointness of each kind, using a general theorem on conservation law (Ibragimov, 2007), we establish the conservation laws corresponding to every Lie point symmetry obtained. In addition, some exact solutions are constructed.