  This paper is concerned with the existence and the stability of travelling
wave solutions to a bistable reaction-diffusion equation with a jump
discontinuious point on nonlinear term. Sub-super solution method is used
throughout this paper. As a matter of fact, this nonlinear discontinuity term
is frequently emerging when study the travelling wave solution of
reaction-diffusion-ODE systems. Hence, it is meaningful to consider this kind
of problem.
