Uniqueness of travelling waves for nonlocal monostable equations

We consider a nonlocal analogue of the Fisher-KPP equation u(t) = J* u - u + f(u); x is an element of R, f(0) = f(1) = 0, f > 0 on (0, 1), and its discrete counterpart (u) over dot(n) = (J * u)(n) - u(n) + f(u(n)), n is an element of Z, and show that travelling wave solutions of these equations that are bounded between 0 and 1 are unique up to translation. Our proof requires finding exact a priori asymptotics of a travelling wave. This we accomplish with the help of Ikehara's Theorem (which is a Tauberian theorem for Laplace transforms).